Question

There are 32 female performers in a dance recital. The ratio of men to women is 3:8. How many men are in the dance recital?

Answer 1

3:8
x4

12:32

The answer is 12 men.

Since the ratio is 3 men to 8 women, and there Are 32 WOMEN, WE NEED TO MULTIPLY BOTH SIDES OF THE RATIO BY 4 FOR OUR RATIO TO BE EQUAL TO OUR OLD RATIO. 3X4=12 AND 8X4=32. THIS RATIO IS TELLING US THAT IF THERE ARE 32 WOMEN, THERE WILL BE 12 MEN.

THERE ARE 12 MEN IN THE DANCE RECITAL.

Answer 2

Let

x------> number of men in the dance recital

y------> number of women in the dance recital

we know that

`(x)/(y) =(3)/(8)` -------> equation
`1`

`y=32` -------> equation
`2`

Substitute equation
`2` in equation
`1`

`(x)/(32) =(3)/(8) \\\\ x=(32*3)/(8)`

`x=12\ men`

therefore

the answer is

There are
`12\ men` in the dance recital