Algebra Choir Ratio Problem.

Question

The ratio of females to males in the choir is 7 to 4. If twelve males and three females are absent from a particular practice, the ratio of females and males is five to two. How many members of the choir attended this particular practice?

Answer 1

We are giving the ratios of number of females to males in a choir in two different situations. Say f is the number of females and m is the number of males in the choir. Then we have:

f / m = 7 / 4 when everyone is presents

(f-3) / (m-12) = 5 / 2 when 3 females and 12 males are missing.

This gives us two equations and two variables, which we can solve by cross-multiplying each equation.

4f = 7m

5(m-12) = 2(f-3)

I leave it to the student to solve the system. If more support is required, please comment.