Question

Casey paid $\$32$ for a book that was on a sale at $20\%$ off. What was the original price for that book $?$

Answer 1

Find the original price for book:

Let the original price of the book be $\mathrm{x}$.

The rate of discount given to Casey was $20\%$.

We know, $\mathbf{\text{Discount=}}\frac{\mathbf{Original}\mathbf{}\mathbf{price}\mathbf{\times }\mathbf{Discount}\mathbf{}\mathbf{rate}}{\mathbf{100}}$

Calculate the discount given to Casey from the above formula:

$$\begin{gathered} \mathrm{Discount}=\frac{\mathrm{x}\times 20}{100} \\ =\frac{\mathrm{x}}{5} \end{gathered}$$

Price paid by Casey was the difference of Original price and the discount given by:

$$\begin{gathered} \mathrm{Price}\mathrm{paid}\mathrm{by}\mathrm{cassey}=\mathrm{x}-\frac{\mathrm{x}}{5} \\ =\frac{5\mathrm{x}-\mathrm{x}}{5} \\ =\frac{4\mathrm{x}}{5} \end{gathered}$$

Also, Since the price paid by Casey was $\$32$, it follows that:

$$\begin{gathered} \frac{4x}{5}=32 \\ \Rightarrow x=\frac{32\times 5}{4} \\ \Rightarrow x=40 \end{gathered}$$

Hence, the original price for that book was $\mathbf{\$}\mathbf{40}$.