## Related questions with answers

Question

Solve.

After a serious automobile accident, most insurance companies will replace the damaged car with a new one if repair costs exceed $80\%$ of the NADA, or "blue-book," value of the car. Lorenzo's car recently sustained $\$9200$ worth of damage but was not replaced. What was the bluebook value of his car?

Solution

VerifiedStep 1

1 of 2Let $x$ be the blue-book value of the car.

The conditions of the problem translate to

$\begin{align*} 0.80x>9200 .\end{align*}$

Using the properties of inequality, the inequality above is equivalent to

$\begin{align*} 0.80x&>9200 \\ x&>\dfrac{9200}{0.80} \\ x&>11500 .\end{align*}$

Since the car was not replaced, then the blue-book value of the car, $x$ is greater than $\$11,500 .$

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