Q23. - Algebra 1

Question

CARS Beng is shopping for a car. The cost of a new car is $15,500. This is 25% greater than the cost of a used car. What is the cost of the used car?

Step-by-Step Solution

Answer

The cost of the used car is $11,625.

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

Step 2. Example of the percentage change.

For example, if a person has 25 dollars and he gets 3 more dollars and now has 28 dollars, its percentage increase is calculated as shown:

 $\begin{array}{l}\text{Increase }=28-25=3\\ \%\text{ change = r, then}\\ \frac{3}{25}=\frac{r}{100}\\ r=\frac{3}{25}\times 100\\ =12\%\end{array}$

Step 3. Find the percentage change.

We are given that the cost of a new car is $15,500.

The cost of a new car is 25% greater than the cost of a used car.

If we let x represent the cost of the used car then, we can find the amount of change using the percentage change as follows:

$x=\text{Cost of new car - 25\%}\times \text{Cost of new car}$

Thus, plugging values we have: 

$\begin{array}{l}x=\$15500-\frac{25}{100}\times \$15500\\ x=15500-0.25\times 15500\\ x=15500-3875\\ x=\$11625\end{array}$

 Thus, the cost of the used car is $11,625.