Q2A. - Algebra 1

Question

A music store has sold $\frac{3}{5}$ of their hip-hop CDs, but 10 were returned. Now the store has 62 hip-hop CDs. How many were there originally?

Step-by-Step Solution

Answer

The number of hip-hop CDs in the music store were 130.

Step 1. Make the equation.

Assume that the total hip-hop CDs in the store is x.

The number of CDs sold is $\frac{3}{5}x$.

Remaining CDs are $\frac{2}{5}x$.

Also 10 CDs were returned. Now the equation is $\frac{2}{5}x+10=62$.

Step 2. Isolate the variable.

$\begin{array}{l}\frac{2}{5}x+10=62\\ \frac{2}{5}x=62-10\\ \frac{2}{5}x=52\end{array}$

Step 3. Find the value of x from the equation.

$\begin{array}{l}2x=52\times 5\\ 2x=260\\ x=\frac{260}{2}\\ x=130\end{array}$

Thus, the number of hip-hop CDs in the music store were 130.