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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 $5,300 for repairs on her car
after an accident. vhat can be concluded about the blue-book value of the car?

In this problem, we are asked to determine what can be concluded about the "blue-book" value of Michelle's car given that her insurance company paid $5,300 for repairs. We know that insurance companies will replace a vehicle if the repair cost exceeds 80% of the blue-book value.

### Let’s break down the situation:

1. The insurance company paid $5,300 for repairs.
2. The repairs did not exceed 80% of the blue-book value; otherwise, the insurance company would have replaced the car instead of repairing it.

We can now set up an inequality:

\[
5300 \leq 0.80 \times \text{blue-book value}.
\]

Let $ x $ represent the blue-book value of Michelle's car. The inequality becomes:

\[
5300 \leq 0.80x.
\]

To solve for $ x $, we divide both sides of the inequality by 0.80:

\[
x \geq \frac{5300}{0.80}.
\]

Now, let’s calculate:

\[
x \geq 6625.
\]

### Conclusion:
The blue-book value of Michelle's car must be at least **$6,625**. Therefore, the inequality to describe the blue-book value is:

\[
x \geq 6625.
\]

Would you like more details or have any questions?

### Related Questions:
1. What would happen if the repair cost had been $7,000?
2. If the blue-book value is exactly $8,000, how much could the insurance company pay for repairs before replacing the car?
3. How does the insurance company calculate the percentage of repairs relative to the blue-book value?
4. Can the blue-book value fluctuate after repairs have been made to the car?
5. How might depreciation affect the blue-book value of the car after the accident?

### Tip:
Always make sure you know the percentage of repair costs relative to a vehicle's value to avoid unexpected replacement situations in car insurance policies.

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 $5,300 for repairs on her car after an accident. What can be concluded about the blue-book value of the car?

Find out how to calculate the minimum blue-book value of a car based on repair costs and percentage thresholds. In this problem, Michelle's insurance company paid $5,300 in repairs, and you will use inequalities to determine the blue-book value. Suitable for Grades 7-9, this problem involves algebra and percentages.

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