Chapter 1.1, Problem 51E

To determine

To determine the number of students marching in the band.

Answer to Problem 51E

71

Explanation of Solution

Given:

One sixth of the girls and two sevenths of the boys in a school marching band are in the percussion section.

Calculation:

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

There are 6 girls in the percussion band, which is one sixth of the total number of girls in the marching band.

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

There are 10 boys in the percussion band, which is two sevenths of the total number of boys in the marching band.

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

Thus, the total number of students in the marching band is the total number of boys and girls in the band.

  $\Rightarrow x+y=36+35=71$

Conclusion:

Therefore, there are 71 students in the marching band.