Question

Kim bought a pair of shoes on sale for $\$40.50.$ The sale price was $45\%$ of the original price. What was the original price of the shoes?

Short answer

The original price of the shoes is$\$90.$

Step-by-step solution

Step 1. Given Information 

Kim bought a pair of shoes on sale for $\$40.50$and the sale price was$45\%$of the original price. We have to find the original price of the shoes.

Step 2. Translate into an equation 

Let xbe the original price of the shoes.

Now, the sale price $45\%$of the original price is $\$40.50$

So, the equation is

$\left(45\%\right)·x=40.50$

Step 3. Solve the equation  

By proceeding with the calculation further

$$\begin{gathered} \left(45\%\right)·x=40.50 \\ \left(0.45\right)·x=40.50 \\ x=\frac{40.50}{0.45} \\ x=90 \end{gathered}$$

Step 4. Check the answer 

So, yes $45\%\mathrm{of}90\mathrm{is}40.50.$

Thus, the original price of the shoes is$\$90.$