Chapter 1.7, Problem 35E

To determine

To find: the cost of sweater including the sales tax.

Answer to Problem 35E

$47.92

Explanation of Solution

Given information:

  $\begin{array}{c}p=\$59.99\\ D\left(p\right)=25\%\text{ off }p\\ t\left(D\left(p\right)\right)=6.5\%\text{ of }\left(D\left(p\right)\right)\\ C\left(p\right)=\text{Total cost}\end{array}$

Here, $p$ is the original price, $D\left(p\right)$ is discounted price, $t\left(p\right)$ represents sales tax, and $C\left(p\right)$ represents the total cost in dollars.

Calculation:

The equation for total cost of sweater is as follows:

  $C\left(p\right)=D\left(p\right)+t\left(D\left(p\right)\right)\text{\& }\mathrm{...}\left(1\right)$

The discounted prices function can be evaluated as follows:

  $\begin{array}{c}D\left(p\right)=25\%\text{ off }p\\ =100\%p-25\%p\\ =75\%p\\ =\frac{75}{100}p\\ =0.75p\\ =0.75\left(\$59.99\right)\left[\text{Pluging value of }p\right]\\ =\$44.9925\end{array}$

Now, evaluate the $t\left(D\left(p\right)\right)$ as follows:

  $\begin{array}{c}t\left(D\left(p\right)\right)=6.5\%\left(D\left(p\right)\right)\\ =0.065\left(D\left(p\right)\right)\\ =0.065\left(\$44.9925\right)\left[\text{Plug in the value of }D\left(p\right)\right]\\ =\$2.9245125\end{array}$

Substitute the value of $D\left(p\right)$ and $t\left(D\left(p\right)\right)$ in equation (1) and evaluate $C\left(p\right)$ as shown below.

  $\begin{array}{c}C\left(p\right)=D\left(p\right)+t\left(D\left(p\right)\right)\\ =\$44.9925+\$2.9245125\\ =\$47.9170125\\ =\$47.92\left[\text{Round off value}\right]\end{array}$

Thus the cost of sweater including the sales tax is $47.92.