Question

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

Three-fifths of the members of the school choir are women. If there are $24$women, what is the total number of choir members?

Short answer

The total number of choir members is $40$.

Step-by-step solution

Step 1. Given Information

We are given that there are $24$women in the school choir.

We have to find the total number of choir members.

Step 2. Forming the equation

Let the total number of choir members be x,

We know that,

$\frac{3}{5}$of total choir members $=24$

So, the equation will be,

$$\begin{gathered} \frac{3}{5}\times x=24 \\ \frac{3}{5}x=24 \end{gathered}$$

Step 3. Solving the equation

Solving the equation,

$\frac{3}{5}x=24$

Multiplying both sides by $\frac{5}{3}$,

$$\begin{gathered} \frac{5}{3}·\frac{3}{5}x=\frac{5}{3}·24 \\ x=5\times 8 \\ x=40 \end{gathered}$$

The total number of choir members is $40$.

Step 4. Checking the solution

Putting the value of xin the equation, we get

$$\begin{gathered} \frac{3}{5}\left(40\right)=24 \\ 3\times 8=24 \\ 24=24 \\ \text{LHS}=\text{RHS} \end{gathered}$$

Hence the solution is correct.