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Let's break down the problem from your image step by step.

### Part a:

You are given that a person has a car insurance policy with:
- A **$800 deductible**.
- The person files claims for **$540** and **$1000** during a two-year period.
- The **annual premium** for the policy is **$550**.

#### With insurance:
- The first claim is $540. Since the deductible is $800, the insurance company doesn't pay anything, and the person has to cover the entire $540.
- The second claim is $1000. Since the deductible is $800, the person pays $800, and the insurance company covers the remaining $200.

Total cost with insurance:
- **Claims paid by the person**: $540 + $800 = **$1340**.
- **Total premiums over two years**: 2 × $550 = **$1100**.
- **Total cost with insurance**: $1340 + $1100 = **$2440**.

This explains why the answer for the total cost with insurance in part (a) is **$2440**.

#### Without insurance:
- The person would pay the full amount of the claims.
- Total amount of claims = $540 + $1000 = **$1540**.

So, the answer for the total cost without insurance in part (a) is **$1540**.

### Part b:

You are given that a person has a car insurance policy with:
- A **$300 deductible**.
- The person files claims for **$540** and **$1400** during a two-year period.
- The **annual premium** for the policy is **$780**.

#### With insurance:
- The first claim is $540. Since the deductible is $300, the person pays $300, and the insurance company covers the remaining $240.
- The second claim is $1400. Since the deductible is $300, the person pays $300, and the insurance company covers the remaining $1100.

Total cost with insurance:
- **Claims paid by the person**: $300 + $300 = **$600**.
- **Total premiums over two years**: 2 × $780 = **$1560**.
- **Total cost with insurance**: $600 + $1560 = **$2160**.

#### Without insurance:
- The person would pay the full amount of the claims.
- Total amount of claims = $540 + $1400 = **$1940**.

So, the answers for part (b) would be:
- **With insurance**: $2160.
- **Without insurance**: $1940.

Would you like further details or clarifications?

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Here are 5 related questions to deepen understanding:

1. How does changing the deductible affect the total amount paid by the policyholder?
2. What would happen if the claims exceed the deductible by a larger amount?
3. How do insurance premiums impact the decision to choose a high or low deductible?
4. What other factors could influence the total cost of insurance, besides claims and deductibles?
5. What if a person doesn’t file any claims—how does the premium-only cost compare?

**Tip:** Always consider both the deductible and premium when evaluating the total cost of an insurance policy.

A person has a car insurance policy with a $300 deductible provision (per claim) for collisions. During a two-year period, the person files claims for $540 and $1400. The annual premium for the policy is $780. With the insurance policy, the person would pay $X. Without the insurance policy, the person would pay $Y.

Learn how to calculate the total costs for car insurance with a $300 deductible and $780 annual premium. Understand the difference in payments with and without insurance for claims of $540 and $1400. Suitable for students in Grades 9-10.

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