Chapter 1.1, Problem 51E

To determine

To calculate: Total number of students in the marching band.

Answer to Problem 51E

The number of students in the marching band is 71.

Given information: One-sixth of the girls and two-seventh of the boys of a school marching band are in percussion section. Number of girls in the percussion section is 6 and number of boys is 10.

Calculation:

Let total number of girls in the marching band be x and number of boys be y.

  $\frac{1}{6}$ th of x is 6 and $\frac{2}{7}$ th of y is 10.

It can be expressed as,

  $\begin{array}{l}\frac{1}{6}\times x=6\\ \Rightarrow x=6\times 6\\ \Rightarrow x=36\end{array}$

And also,

  $\begin{array}{l}\frac{2}{7}\times y=10\\ \Rightarrow y=10\times \frac{7}{2}\\ \Rightarrow y=\frac{10\times 7}{2}\\ \Rightarrow y=\frac{70}{2}\\ \Rightarrow y=35\end{array}$

Number of girls in the marching band = 36, number of boys = 35.

Total number of students in the marching band = $(36+35)=71$ .

Explanation of Solution

Given information: One-sixth of the girls and two-seventh of the boys of a school marching band are in percussion section. Number of girls in the percussion section is 6 and number of boys is 10.

Calculation:

Let total number of girls in the marching band be x and number of boys be y.

  $\frac{1}{6}$ th of x is 6 and $\frac{2}{7}$ th of y is 10.

It can be expressed as,

  $\begin{array}{l}\frac{1}{6}\times x=6\\ \Rightarrow x=6\times 6\\ \Rightarrow x=36\end{array}$

And also,

  $\begin{array}{l}\frac{2}{7}\times y=10\\ \Rightarrow y=10\times \frac{7}{2}\\ \Rightarrow y=\frac{10\times 7}{2}\\ \Rightarrow y=\frac{70}{2}\\ \Rightarrow y=35\end{array}$

Number of girls in the marching band = 36, number of boys = 35.

Total number of students in the marching band = $(36+35)=71$ .