most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of the "blue-book" value of the vehicle. Michelles insurance company paid $7,500 for repairs on her car after an accident. what can be concluded about the blue-book value of the car?

Since Michelle's insurance company paid $7,500 for repairs, and insurance companies typically replace a vehicle if repair costs exceed 80% of the vehicle's blue-book value, we can set up an inequality to estimate the car's blue-book value.

Let the blue-book value of the car be $ x $. The condition given is that repairs should be less than or equal to 80% of the blue-book value, i.e.,

\[
7500 \leq 0.80x
\]

To find the blue-book value, solve for $ x $:

\[
x \geq \frac{7500}{0.80} = 9375
\]

Thus, the blue-book value of Michelle's car must be at least **$9,375**.

Would you like a more detailed breakdown or further clarification?

Here are 5 related questions:
1. How is the blue-book value of a car determined?
2. What happens if the repair cost exceeds 80% of the blue-book value?
3. Why do insurance companies use a threshold of 80%?
4. How does depreciation affect the blue-book value of a car?
5. How do insurance companies estimate repair costs after an accident?

**Tip:** Always ask for a detailed breakdown of your insurance coverage to avoid surprises when making claims.

Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of the 'blue-book' value of the vehicle. Michelle's insurance company paid $7,500 for repairs on her car after an accident. What can be concluded about the blue-book value of the car?

This problem helps you estimate the blue-book value of Michelle's car based on repair costs exceeding 80% of the value. It covers key algebraic concepts, inequality, and percentage calculation, making it suitable for students in Grades 8-10.

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