Chapter 1.4, Problem 4MCQ

To determine

To find: original price of the jacket using composition of function.

Answer to Problem 4MCQ

  $\$62.22$

Explanation of Solution

Given information: Off on jacket = 33%

Sales tax = 5.5%

Money paid for jacket = $45.95

Calculation:

Let the original price, discount price and total amount paid be $p,D\left(p\right)$ and $T\left(D\left(p\right)\right)$ .

If jacket is 30% off, the discount price is 70% of the original price, and it can be evaluated as follows:

  $\begin{array}{c}D\left(p\right)=70\%p\\ =\frac{70}{100}p\\ =0.7p\end{array}$

The total amount paid is the sum of $D\left(p\right)$ and tax on $D\left(p\right)$ .It can be evaluated as follows:

  $\begin{array}{c}T\left(D\left(p\right)\right)=D\left(p\right)+5.5\%D\left(p\right)\\ =D\left(p\right)+0.055D\left(p\right)\\ =1.055D\left(p\right)\end{array}$

Substitute the value of $T\left(D\left(p\right)\right)$ and $D\left(p\right)$ in the above equation and evaluate as follows:

  $\begin{array}{c}\$45.95=1.055\left(0.7p\right)\\ \$45.95=0.7385p\\ p=\frac{\$45.95}{0.7385}\\ =\$62.22\end{array}$

Thus, the original price is $\$62.22$ .