Chapter 7, Problem 4STP

To determine

To Find:

The selling price of the car.

Answer to Problem 4STP

H

Explanation of Solution

Given Information:

Kay bought a used car.The sales tax rate was 6.5% of the selling price , and she also had to pay $325 in registration fees.She spent total of $15,501.25 on buying the car.

Calculation:

  $\begin{array}{l}Given\\ Sales\text{ tax rate = 6}\text{.5\% of the selling price}\\ \text{Kay paid for registration fees = \$325}\\ \text{Total amount Kay spent =\$15,501}\text{.25}\\ \\ \text{Let }\\ The\text{ selling price of the car = s}\\ \text{Cost of car including the sales tax = s + 6}\text{.5\%(s)=(100+6}\text{.5)\%(s)=1}\text{.065s}\\ \text{Total price of car that Kay paid including registration fees = 1}\text{.065s + 325}\\ \text{So, }\\ P(s)=\text{1}\text{.065}s\text{ + 325}\\ \text{and P(s)= 15,501}\text{.25}\\ \text{Substitute the value in the equation and solve for s:}\\ \Rightarrow 15,501.25=\text{1}\text{.065}s\text{ + 325}\\ \Rightarrow \text{1}\text{.065s = 15,501}\text{.25 - 325}\mathrm{..........}\text{[subtract 325 from each side]}\\ \Rightarrow \text{1}\text{.065s = 15,176}\text{.25}\\ \Rightarrow \text{s = }\frac{\text{15,176}\text{.25}}{\text{1}\text{.065}}\mathrm{..........................}[\text{divide each side by 1}\text{.065}]\\ \Rightarrow s=14,250\\ So,\text{ the selling price of the car is \$14,250}\text{.}\\ \text{Hence , H is the correct option}\text{.}\end{array}$