Some word problems

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of dental policyholders is three times the number of vision policyholders. [/example] [solution] Let $v$ be the number of vision policyholders. Let $d$ be the number of dental policyholders. Then the relationship is: $d = 3v$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: There are twice as many travel insurance clients as accident insurance clients. [/example] [solution] Let $a$ be the number of accident insurance clients. Let $t$ be the number of travel insurance clients. Then the relationship is: $t = 2a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of cyber liability policyholders equals five times the number of commercial property policyholders. [/example] [solution] Let $c$ be the number of commercial property policyholders. Let $y$ be the number of cyber liability policyholders. Then the relationship is: $y = 5c$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: For every 1 person with a disability policy, there are 8 people with life insurance. [/example] [solution] Let $d$ be the number of people with a disability policy. Let $l$ be the number of people with life insurance. Then the relationship is: $l = 8d$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of fire insurance claims is one-fourth the number of flood insurance claims. [/example] [solution] Let $f$ be the number of flood insurance claims. Let $r$ be the number of fire insurance claims. Then the relationship is: $r = \frac{1}{4}f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: There are six times as many renters insurance holders as boat insurance holders. [/example] [solution] Let $b$ be the number of boat insurance holders. Let $r$ be the number of renters insurance holders. Then the relationship is: $r = 6b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of insured vehicles is double the number of insured homes. [/example] [solution] Let $h$ be the number of insured homes. Let $v$ be the number of insured vehicles. Then the relationship is: $v = 2h$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: There are three times fewer yacht insurance clients than motorcycle insurance clients. [/example] [solution] Let $m$ be the number of motorcycle insurance clients. Let $y$ be the number of yacht insurance clients. Then the relationship is: $y = \frac{1}{3}m$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of mobile home policyholders is nine times the number of RV policyholders. [/example] [solution] Let $r$ be the number of RV policyholders. Let $m$ be the number of mobile home policyholders. Then the relationship is: $m = 9r$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: For every two policyholders with earthquake coverage, there are ten with wind damage coverage. [/example] [solution] Let $e$ be the number of earthquake coverage policyholders. Let $w$ be the number of wind damage coverage policyholders. Then the relationship is: $w = 5e$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: The number of health insurance policyholders is four times the number of individuals with supplemental coverage. [/example] [solution] Let $s$ be the number of individuals with supplemental coverage. Let $h$ be the number of health insurance policyholders. Then the relationship is: $h = 4s$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: There are seven times as many insured homeowners as there are renters with insurance. [/example] [solution] Let $r$ be the number of insured renters. Let $h$ be the number of insured homeowners. Then the relationship is: $h = 7r$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: For every pet insurance policy, there are five auto insurance policies. [/example] [solution] Let $p$ be the number of pet insurance policies. Let $a$ be the number of auto insurance policies. Then the relationship is: $a = 5p$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: The number of flood claims is one-fifth the number of fire claims. [/example] [solution] Let $f$ be the number of fire claims. Let $l$ be the number of flood claims. Then the relationship is: $l = \frac{1}{5}f$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: The total number of group life policyholders is three times greater than the number of individual policyholders. [/example] [solution] Let $i$ be the number of individual policyholders. Let $g$ be the number of group life policyholders. Then the relationship is: $g = 3i$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: There are twice as many claim adjusters as underwriters at the company. [/example] [solution] Let $u$ be the number of underwriters. Let $c$ be the number of claim adjusters. Then the relationship is: $c = 2u$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: The number of disability insurance recipients is half the number of long-term care recipients. [/example] [solution] Let $l$ be the number of long-term care recipients. Let $d$ be the number of disability insurance recipients. Then the relationship is: $d = \frac{1}{2}l$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: There are ten times as many policies in force as there are policies pending approval. [/example] [solution] Let $p$ be the number of policies pending approval. Let $f$ be the number of policies in force. Then the relationship is: $f = 10p$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: The number of corporate clients is three-quarters the number of individual clients. [/example] [solution] Let $i$ be the number of individual clients. Let $c$ be the number of corporate clients. Then the relationship is: $c = \frac{3}{4}i$ [/solution]

[example] [extitle] Problem %counter% [/extitle]

Translate the following into an algebraic expression: There are four times more insured motorcycles than insured scooters. [/example] [solution] Let $s$ be the number of insured scooters. Let $m$ be the number of insured motorcycles. Then the relationship is: $m = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Greenfield Insurance, the number of auto insurance policyholders is five times the number of renters insurance policyholders. [/example]

[solution] Let $r$ be the number of renters insurance policyholders. Let $a$ be the number of auto insurance policyholders. Then the relationship is: $a = 5r$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: In 2024, the total number of life insurance claims filed was three times the number of disability claims. [/example]

[solution] Let $d$ be the number of disability claims. Let $l$ be the number of life insurance claims. Then the relationship is: $l = 3d$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The Claims Department reported that flood insurance claims were one-fourth the amount of fire insurance claims last year. [/example]

[solution] Let $f$ be the number of fire insurance claims. Let $l$ be the number of flood insurance claims. Then the relationship is: $l = \frac{1}{4} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: For every insured commercial property, there are eight insured residential properties in the portfolio. [/example]

[solution] Let $c$ be the number of insured commercial properties. Let $r$ be the number of insured residential properties. Then the relationship is: $r = 8c$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Beacon Insurance, the number of health insurance holders is twice the number of supplemental insurance holders. [/example]

[solution] Let $s$ be the number of supplemental insurance holders. Let $h$ be the number of health insurance holders. Then the relationship is: $h = 2s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The ratio of boat insurance policies to motorcycle insurance policies is 1 to 6. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $m$ be the number of motorcycle insurance policies. Then the relationship is: $m = 6b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: According to the annual report, disability insurance recipients were half the number of long-term care recipients. [/example]

[solution] Let $l$ be the number of long-term care recipients. Let $d$ be the number of disability insurance recipients. Then the relationship is: $d = \frac{1}{2} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of renters insured by Maple Leaf Insurance is nine times the number of boat insurance holders. [/example]

[solution] Let $b$ be the number of boat insurance holders. Let $r$ be the number of renters insured. Then the relationship is: $r = 9b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: For every 3 travel insurance policies, there are 20 standard health insurance policies in force. [/example]

[solution] Let $t$ be the number of travel insurance policies. Let $h$ be the number of standard health insurance policies. Then the relationship is: $h = \frac{20}{3} t$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The underwriting department states that auto insurance policies are three times as many as home insurance policies. [/example]

[solution] Let $h$ be the number of home insurance policies. Let $a$ be the number of auto insurance policies. Then the relationship is: $a = 3h$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The total number of corporate clients is four times the number of individual clients. [/example]

[solution] Let $i$ be the number of individual clients. Let $c$ be the number of corporate clients. Then the relationship is: $c = 4i$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Silver Shield Insurance, the number of policies pending approval is one-fifth the number of active policies. [/example]

[solution] Let $p$ be the number of policies pending approval. Let $a$ be the number of active policies. Then the relationship is: $p = \frac{1}{5} a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: For every 7 life insurance policies, there are 3 supplemental insurance policies. [/example]

[solution] Let $l$ be the number of life insurance policies. Let $s$ be the number of supplemental insurance policies. Then the relationship is: $s = \frac{3}{7} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of bicycle insurance claims is one-eighth the number of auto insurance claims. [/example]

[solution] Let $a$ be the number of auto insurance claims. Let $b$ be the number of bicycle insurance claims. Then the relationship is: $b = \frac{1}{8} a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The policyholder base for long-term care is five times greater than that of short-term care. [/example]

[solution] Let $s$ be the number of short-term care policyholders. Let $l$ be the number of long-term care policyholders. Then the relationship is: $l = 5s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: There are twice as many renters insurance policies as there are boat insurance policies at OceanView Insurance. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then the relationship is: $r = 2b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of workers compensation claims is three times the number of general liability claims. [/example]

[solution] Let $g$ be the number of general liability claims. Let $w$ be the number of workers compensation claims. Then the relationship is: $w = 3g$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of active health insurance policies is four times the number of supplemental policies in force. [/example]

[solution] Let $s$ be the number of supplemental policies. Let $h$ be the number of active health insurance policies. Then the relationship is: $h = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: For every insured motorcycle, there are ten insured scooters. [/example]

[solution] Let $m$ be the number of insured motorcycles. Let $s$ be the number of insured scooters. Then the relationship is: $s = 10m$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The number of active flood insurance policies is one-third the number of active fire insurance policies. [/example]

[solution] Let $f$ be the number of active fire insurance policies. Let $l$ be the number of active flood insurance policies. Then the relationship is: $l = \frac{1}{3} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Summit Insurance, the number of auto insurance policyholders increased significantly this year and is now reported to be eight times the number of renters insurance policyholders, reflecting a boom in vehicle registrations in the region. [/example]

[solution] Let $r$ be the number of renters insurance policyholders. Let $a$ be the number of auto insurance policyholders. Then the relationship is: $a = 8r$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: During the past fiscal year, the Claims Department noted that the number of life insurance claims filed was nearly five times the number of disability claims, underscoring a shift in claimant demographics. [/example]

[solution] Let $d$ be the number of disability claims. Let $l$ be the number of life insurance claims. Then the relationship is: $l = 5d$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: After extensive review, the risk analysis team reported that flood insurance claims represented approximately one-sixth the volume of fire insurance claims in the last reporting period, reflecting recent weather patterns. [/example]

[solution] Let $f$ be the number of fire insurance claims. Let $l$ be the number of flood insurance claims. Then the relationship is: $l = \frac{1}{6} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: In the company’s real estate portfolio, the count of insured commercial properties is significantly lower than insured residential properties, with the latter being nearly ten times greater. [/example]

[solution] Let $c$ be the number of insured commercial properties. Let $r$ be the number of insured residential properties. Then the relationship is: $r = 10c$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Guardian Health Insurance, the marketing team reported that the number of health insurance holders has doubled compared to the number of supplemental insurance holders in the last quarter. [/example]

[solution] Let $s$ be the number of supplemental insurance holders. Let $h$ be the number of health insurance holders. Then the relationship is: $h = 2s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: According to the latest customer analytics, the ratio of boat insurance policies to motorcycle insurance policies is approximately 1 to 7, highlighting a niche market trend. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $m$ be the number of motorcycle insurance policies. Then the relationship is: $m = 7b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The annual report revealed that recipients of disability insurance were about half as many as those receiving long-term care benefits, a statistic crucial for resource allocation. [/example]

[solution] Let $l$ be the number of long-term care recipients. Let $d$ be the number of disability insurance recipients. Then the relationship is: $d = \frac{1}{2} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Maple Leaf Insurance, the number of renters insured has surged to be nine times the number of boat insurance holders, attributed to the recent housing developments near lakes. [/example]

[solution] Let $b$ be the number of boat insurance holders. Let $r$ be the number of renters insured. Then the relationship is: $r = 9b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The portfolio management team indicated that for every 3 travel insurance policies sold, there are approximately 20 standard health insurance policies currently active, demonstrating the diversity of the insurance products. [/example]

[solution] Let $t$ be the number of travel insurance policies. Let $h$ be the number of standard health insurance policies. Then the relationship is: $h = \frac{20}{3} t$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The underwriting department confirmed that the number of auto insurance policies is three times the number of home insurance policies, reflecting the community’s vehicular growth. [/example]

[solution] Let $h$ be the number of home insurance policies. Let $a$ be the number of auto insurance policies. Then the relationship is: $a = 3h$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: Corporate client accounts have quadrupled the number of individual client accounts at TechSafe Insurance this year due to a new business outreach program. [/example]

[solution] Let $i$ be the number of individual clients. Let $c$ be the number of corporate clients. Then the relationship is: $c = 4i$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: At Silver Shield Insurance, the number of policies pending approval is currently one-fifth of the active policies, a backlog the company aims to reduce next quarter. [/example]

[solution] Let $p$ be the number of policies pending approval. Let $a$ be the number of active policies. Then the relationship is: $p = \frac{1}{5} a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: In the latest quarterly report, for every 7 life insurance policies, there are 3 supplemental insurance policies, indicating steady growth in supplemental coverage. [/example]

[solution] Let $l$ be the number of life insurance policies. Let $s$ be the number of supplemental insurance policies. Then the relationship is: $s = \frac{3}{7} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: The risk management team highlighted that the number of bicycle insurance claims was roughly one-eighth the number of auto insurance claims this year, reflecting changing commuter patterns. [/example]

[solution] Let $a$ be the number of auto insurance claims. Let $b$ be the number of bicycle insurance claims. Then the relationship is: $b = \frac{1}{8} a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: Long-term care policyholders outnumber short-term care policyholders by a factor of five, influencing upcoming policy adjustments at CareFirst Insurance. [/example]

[solution] Let $s$ be the number of short-term care policyholders. Let $l$ be the number of long-term care policyholders. Then the relationship is: $l = 5s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: OceanView Insurance reported that renters insurance policies doubled the number of boat insurance policies sold over the past year, driven by new housing developments. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then the relationship is: $r = 2b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: Workers compensation claims have tripled compared to general liability claims, prompting a review of workplace safety programs. [/example]

[solution] Let $g$ be the number of general liability claims. Let $w$ be the number of workers compensation claims. Then the relationship is: $w = 3g$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: Active health insurance policies outnumber supplemental policies by a factor of four, indicating strong growth in primary coverage plans. [/example]

[solution] Let $s$ be the number of supplemental policies. Let $h$ be the number of active health insurance policies. Then the relationship is: $h = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: Scooter insurance policies currently outnumber motorcycle policies by a factor of ten, reflecting urban commuting trends. [/example]

[solution] Let $m$ be the number of insured motorcycles. Let $s$ be the number of insured scooters. Then the relationship is: $s = 10m$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Translate the following into an algebraic expression: Active flood insurance policies are one-third the number of active fire insurance policies, a trend observed consistently over the past three years. [/example]

[solution] Let $f$ be the number of active fire insurance policies. Let $l$ be the number of active flood insurance policies. Then the relationship is: $l = \frac{1}{3} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The company’s latest quarterly report shows that while overall auto registrations increased by 12%, the number of auto insurance policyholders is currently eight times the number of renters insurance policyholders, despite steady housing market fluctuations. Write an equation that relates the two quantities. [/example]

[solution] Let $r$ be the number of renters insurance policyholders. Let $a$ be the number of auto insurance policyholders. Then the relationship is: $a = 8r$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Over the past year, disability claims have been steadily rising, but life insurance claims have grown even faster. The Claims Department recorded that life insurance claims are five times the number of disability claims. Consider this when modeling claim ratios. Write an equation expressing this relationship. [/example]

[solution] Let $d$ be the number of disability claims. Let $l$ be the number of life insurance claims. Then the relationship is: $l = 5d$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

While investigating seasonal trends, the risk team found flood insurance claims are about one-sixth of fire insurance claims, despite recent flooding events. Given that the fire claims are $f$, write an equation relating flood claims $l$ to $f$. [/example]

[solution] Let $f$ be the number of fire insurance claims. Let $l$ be the number of flood insurance claims. Then the relationship is: $l = \frac{1}{6} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The portfolio management division revealed that residential properties insured vastly outnumber commercial properties, roughly by a factor of ten, which aligns with the company’s strategic focus. Express this with an equation. [/example]

[solution] Let $c$ be the number of insured commercial properties. Let $r$ be the number of insured residential properties. Then the relationship is: $r = 10c$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

At Guardian Health, after rolling out a new marketing campaign, the number of health insurance holders doubled relative to supplemental insurance holders, even as customer service calls remained steady. Write an equation for this relationship. [/example]

[solution] Let $s$ be the number of supplemental insurance holders. Let $h$ be the number of health insurance holders. Then the relationship is: $h = 2s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Boat insurance policies make up a niche segment at the company, trailing motorcycle policies by a factor of seven, even though boat sales spiked during summer. Create an equation connecting boat policies $b$ and motorcycle policies $m$. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $m$ be the number of motorcycle insurance policies. Then the relationship is: $m = 7b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Despite a rise in disability insurance recipients, the number is still half that of long-term care recipients. This ratio is critical for upcoming budget allocations. Express this with an equation. [/example]

[solution] Let $l$ be the number of long-term care recipients. Let $d$ be the number of disability insurance recipients. Then the relationship is: $d = \frac{1}{2} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

New lakeside developments have caused renters insurance numbers to surge. The number of renters insured is now nine times the number of boat insurance holders, despite fluctuating marine market trends. Write an equation to capture this. [/example]

[solution] Let $b$ be the number of boat insurance holders. Let $r$ be the number of renters insured. Then the relationship is: $r = 9b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Travel insurance policies and health insurance policies show differing growth rates; for every 3 travel policies, there are about 20 health policies active. Consider this when modeling policy distributions. Write the equation connecting $t$ and $h$. [/example]

[solution] Let $t$ be the number of travel insurance policies. Let $h$ be the number of health insurance policies. Then the relationship is: $h = \frac{20}{3} t$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The underwriting department reports that the number of auto insurance policies is currently triple the number of home insurance policies, reflecting an increase in urban vehicle ownership. Express this relationship algebraically. [/example]

[solution] Let $h$ be the number of home insurance policies. Let $a$ be the number of auto insurance policies. Then the relationship is: $a = 3h$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Due to a new enterprise initiative, corporate client accounts now number four times the individual accounts. This growth is expected to impact revenue projections. Formulate an equation expressing this. [/example]

[solution] Let $i$ be the number of individual clients. Let $c$ be the number of corporate clients. Then the relationship is: $c = 4i$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Silver Shield Insurance is currently managing a backlog where policies pending approval total one-fifth of all active policies. This metric guides operational priorities. Write an equation for this scenario. [/example]

[solution] Let $p$ be the number of policies pending approval. Let $a$ be the number of active policies. Then the relationship is: $p = \frac{1}{5} a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

In the last quarter, the company sold 7 life insurance policies for every 3 supplemental insurance policies. Sales teams are analyzing these ratios to optimize cross-selling. Express this ratio algebraically. [/example]

[solution] Let $l$ be the number of life insurance policies. Let $s$ be the number of supplemental insurance policies. Then the relationship is: $s = \frac{3}{7} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Data shows bicycle insurance claims comprise about one-eighth of auto insurance claims, despite new cycling initiatives encouraging safer roads. Write the equation linking claims $b$ and $a$. [/example]

[solution] Let $a$ be the number of auto insurance claims. Let $b$ be the number of bicycle insurance claims. Then the relationship is: $b = \frac{1}{8} a$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Long-term care policyholders outnumber short-term care policyholders five to one, which is significant for resource allocation decisions. Write an equation for this relationship. [/example]

[solution] Let $s$ be the number of short-term care policyholders. Let $l$ be the number of long-term care policyholders. Then the relationship is: $l = 5s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

OceanView Insurance noted a doubling in renters insurance policies relative to boat insurance policies over the past year, despite boat sales remaining steady. Write an equation reflecting this growth. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then the relationship is: $r = 2b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Workers compensation claims have recently tripled compared to general liability claims, leading to initiatives for enhanced workplace safety. Form an equation expressing this. [/example]

[solution] Let $g$ be the number of general liability claims. Let $w$ be the number of workers compensation claims. Then the relationship is: $w = 3g$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Active health insurance policies have increased dramatically, now four times the number of supplemental policies, impacting plan management strategies. Write an algebraic expression for this. [/example]

[solution] Let $s$ be the number of supplemental policies. Let $h$ be the number of active health insurance policies. Then the relationship is: $h = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Urban commuting shifts have caused scooter insurance policies to outnumber motorcycle policies by a factor of ten, influencing marketing focus. Write an equation linking scooters $s$ and motorcycles $m$. [/example]

[solution] Let $m$ be the number of insured motorcycles. Let $s$ be the number of insured scooters. Then the relationship is: $s = 10m$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Flood insurance policies consistently represent one-third of fire insurance policies, a ratio that has held steady for three years. Express this relationship in an equation. [/example]

[solution] Let $f$ be the number of active fire insurance policies. Let $l$ be the number of active flood insurance policies. Then the relationship is: $l = \frac{1}{3} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

During a rainy spring, the company noted that although the region received record rainfall, the number of flood insurance claims was surprisingly low, amounting to only one-tenth of the total fire insurance claims filed. Meanwhile, the office coffee machine was frequently broken. Write an equation relating flood claims $l$ and fire claims $f$. [/example]

[solution] Let $f$ be the number of fire insurance claims. Let $l$ be the number of flood insurance claims. Then: $l = \frac{1}{10} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

At Apex Insurance, the sales team celebrated a 20% increase in life insurance policies sold, which now total four times the number of supplemental insurance policies. The office’s new plant, however, still struggles to survive under the dim lighting. Formulate an equation for this relationship. [/example]

[solution] Let $s$ be the number of supplemental insurance policies. Let $l$ be the number of life insurance policies. Then: $l = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The marketing department reports that renters insurance policies at Harbor Insurance are six times the number of boat insurance policies, despite the fact that half of the staff still prefer tea over coffee. Write the equation linking renters $r$ and boats $b$. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then: $r = 6b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

During the last quarter, although customer service calls increased by 15%, the ratio of auto insurance policies to home insurance policies at Central Coverage remains steady, with autos being three times as many. A motivational poster in the break room encourages teamwork daily. Write the algebraic relationship. [/example]

[solution] Let $h$ be the number of home insurance policies. Let $a$ be the number of auto insurance policies. Then: $a = 3h$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Despite rumors of a new office dress code, the insurance analytics team found that disability insurance recipients are still half as many as long-term care recipients. Also, the company snack supply was replenished just last week. Create an equation for this ratio. [/example]

[solution] Let $l$ be the number of long-term care recipients. Let $d$ be the number of disability insurance recipients. Then: $d = \frac{1}{2} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The recent tech upgrades haven’t affected sales much, but the underwriting division confirmed that health insurance holders outnumber supplemental insurance holders two to one. Meanwhile, the lobby fountain has been undergoing maintenance for three weeks. Express this relationship algebraically. [/example]

[solution] Let $s$ be the number of supplemental insurance holders. Let $h$ be the number of health insurance holders. Then: $h = 2s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

At Lakeview Insurance, although the fishing derby was canceled due to weather, renters insurance policies surged to nine times the number of boat insurance policies. The company mascot’s costume was cleaned yesterday. Write the corresponding equation. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then: $r = 9b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Even with a power outage causing minor delays, the claims department states that workers compensation claims have tripled compared to general liability claims. The office plants managed to survive the outage. Write an equation relating workers compensation claims $w$ and general liability claims $g$. [/example]

[solution] Let $g$ be the number of general liability claims. Let $w$ be the number of workers compensation claims. Then: $w = 3g$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Though the vending machine is out of order, data shows scooter insurance policies outnumber motorcycle policies by a factor of ten. A new office calendar is hanging next to the water cooler. Express this mathematically. [/example]

[solution] Let $m$ be the number of insured motorcycles. Let $s$ be the number of insured scooters. Then: $s = 10m$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Sales reports indicate flood insurance policies are about one-third the number of fire insurance policies. Meanwhile, the recent team-building exercise involved a pizza party. Write the algebraic equation. [/example]

[solution] Let $f$ be the number of fire insurance policies. Let $l$ be the number of flood insurance policies. Then: $l = \frac{1}{3} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

In the midst of busy conference preparations, it was noted that corporate client accounts now outnumber individual accounts by four times. The office coffee machine broke down again. Write an equation reflecting this fact. [/example]

[solution] Let $i$ be the number of individual clients. Let $c$ be the number of corporate clients. Then: $c = 4i$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The snack room was restocked, but analysts still focus on the ratio of travel insurance to health insurance policies: for every 3 travel policies, there are 20 health policies. Write an equation for this relationship. [/example]

[solution] Let $t$ be the number of travel insurance policies. Let $h$ be the number of health insurance policies. Then: $h = \frac{20}{3} t$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Despite the parking lot renovations, the number of life insurance policies is four times the number of supplemental insurance policies sold. The annual holiday party is scheduled next month. Express the ratio algebraically. [/example]

[solution] Let $s$ be the number of supplemental insurance policies. Let $l$ be the number of life insurance policies. Then: $l = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Although the office thermostat is frequently adjusted, renters insurance policies have doubled the number of boat insurance policies. The IT department is working on faster internet this week. Write an equation representing this. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then: $r = 2b$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The company garden was recently replanted, yet disability insurance recipients remain half as numerous as long-term care recipients. An employee fundraiser is underway this week. Write an equation capturing this ratio. [/example]

[solution] Let $l$ be the number of long-term care recipients. Let $d$ be the number of disability insurance recipients. Then: $d = \frac{1}{2} l$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

With holiday decorations still up, the marketing team noted that active health insurance policies outnumber supplemental policies by four to one, influencing upcoming campaign plans. Write an equation for this relationship. [/example]

[solution] Let $s$ be the number of supplemental policies. Let $h$ be the number of active health insurance policies. Then: $h = 4s$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The company mascot costume was cleaned recently, yet scooter insurance policies have surged to ten times the number of motorcycle policies, reflecting new urban transport trends. Express this in an equation. [/example]

[solution] Let $m$ be the number of insured motorcycles. Let $s$ be the number of insured scooters. Then: $s = 10m$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

Even though the office fountain is temporarily dry, flood insurance policies remain steady at one-third the number of fire insurance policies, a trend over multiple years. Write the equation expressing this. [/example]

[solution] Let $f$ be the number of fire insurance policies. Let $l$ be the number of flood insurance policies. Then: $l = \frac{1}{3} f$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

After a brief internet outage, workers compensation claims were reported to be triple the number of general liability claims. Office plants survived the outage unharmed. Form an equation for this ratio. [/example]

[solution] Let $g$ be the number of general liability claims. Let $w$ be the number of workers compensation claims. Then: $w = 3g$ [/solution]

[example] [extitle]Problem %counter%[/extitle]

The conference room projector was fixed just in time for a meeting where it was revealed that renters insurance policies outnumber boat insurance policies by a factor of six, despite steady boat sales. Write an equation relating renters $r$ and boats $b$. [/example]

[solution] Let $b$ be the number of boat insurance policies. Let $r$ be the number of renters insurance policies. Then: $r = 6b$ [/solution]