Chapter 6.2, Problem 28HP

To determine

To find: Number of boys volunteers and number of girls volunteers.

Answer to Problem 28HP

Number of girls volunteers =25

Number of boys volunteers =35

Explanation of Solution

Given information:

Total number of volunteers = 60

Ration of boys to girls = $7:5$

Let x be the number of boys.

Therefore

Number of girls = $60-x$ .

  $\Rightarrow$ ratio of boys to girls = $\frac{x}{60-x}$

Given ratio of boys to girls = $\frac{7}{5}$

  $\Rightarrow \frac{7}{5}=\frac{x}{60-x}$

On cross multiplication

We get

  $\begin{array}{l}\Rightarrow 7\left(60-x\right)=5x\\ \Rightarrow 7\left(60\right)-7x=5x\\ \Rightarrow 7x+5x=420\\ \Rightarrow 12x=420\\ \Rightarrow x=\frac{420}{12}\\ \Rightarrow x=35\end{array}$

Therefore

Number of boys =35

  $\Rightarrow$ Number of girls = $60-35=25$

Therefore

Number of girls volunteers =25

Number of boys volunteers =35