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:

`(M)/(W)=(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:

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

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

`M=(3)/(5)W=(3)/(5)\cdot20=12`

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