In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

Bill found a book he wanted on sale for \($20.80$. The original price of the book was \)$32$.

The original price of the book was $$32$and its price during sale is $$20.80$.

The objective is to find the amount of discount and discount rate.

The discount is the difference between the original price and the sale price. So the amount of discount for the book is given as

$$\begin{gathered} d=32-20.80 \\ d=11.2 \end{gathered}$$

As the amount of discount $$11.2$is less than the original price $$32$, so it makes sense.

Thus the amount of discount on the book is $$11.2$.

Let $r$be the discount rate.

The discount of $$11.2$is what percent of $$32$, can be written in terms of equation as

$11.2=r·32$

Now divide both sides by $32$.

$\begin{array}{rcl}\frac{11.2}{32}& =& \frac{32r}{32}\\ 0.35& =& r\end{array}$

Thus the discount rate is$0.35$or$35\%$.

Find $35\%$of $32$.

$\begin{array}{rcl}35\%of32& =& 0.35·32\\ & =& 11.2\end{array}$

As it is equal to $11.2$, so our answer is correct.

Hence the solution is checked.