Chapter 6.5, Problem 13PPS

To determine

To write the system of equations and solve to find the number of girls and boys in band third period.

Answer to Problem 13PPS

Girls: 29

Boys: 11

Explanation of Solution

Given:

Number of students in bandthird period: 40

Number of girls is 4 less than 3 times the number of boys.

Calculation:

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

There are 40 students in band third period.

  $\Rightarrow x+y=\mathrm{40............}(1)$

The number of girls is 4 less than 3 times the number of boys.

  $\Rightarrow x=3y-\mathrm{4...........}(2)$

Substitute the value of x in equation (1),

  $\begin{array}{l}\Rightarrow (3y-4)+y=40\\ \Rightarrow 3y-4+y=40\\ \Rightarrow 4y=44\\ \Rightarrow y=11\end{array}$

Substitute the value of y in equation (2),

  $\begin{array}{l}\Rightarrow x=3(11)-4\\ \Rightarrow x=33-4\\ \Rightarrow x=29\end{array}$

Conclusion:

Therefore, the number of boys in the band third period is 11 and the number of girls in the band third period is 29.