Question

There was a concert held at the park. For every 3 men there were 5 women at the concert, if 32 total people attended the concert how many men and women each attended the concert?

Answer 1

We have to find how many men and women attended the concert.

We know that there where 3 men for every 5 woman, so if we divide the amount of men (M) by the amount of women (W) in the concert, we would get:

$\frac{M}{W}=\frac{3}{5}$

We also know that a total of 32 people attended the concert. This total is the sum of the amount men and women in the concert, so we can write:

$M+W=32$

If we rewrite the first equation to clear the value of M and replace it in the second equation we can calculate W as:

$\frac{M}{W}=\frac{3}{5}\Rightarrow M=\frac{3}{5}W$$\begin{gathered} M+W=32 \\ \frac{3}{5}W+W=32 \\ (\frac{3}{5}+1)W=32 \\ \frac{3+5}{5}\cdot W=32 \\ \frac{8}{5}W=32 \\ W=32\cdot\frac{5}{8} \\ W=20 \end{gathered}$

We can now use any of the 2 equations to find the value of M:

$M=\frac{3}{5}W=\frac{3}{5}\cdot20=12$

Answer: there where 12 men and 20 women at the concert.