Question

The ratio of men to women in a movie theater is 3:5. As two more men and one more woman walk in, the ratio of men to women becomes 2:3. How many women were in the theater before these three walked in?

Answer 1

Answer: no of women before they walked in is 8.

Explanation:

given data:

ratio of men and women = 3:5

when 2 men and 1 woman walks in = 2:3

solution:

no of women in the theatre before they walked in

men/women= 3/2,

let men =3x............eqn1

women = 2x................eqn2

Total =20

therefore:

`3x+2x=20`

collect like terms

`5x=20`

`x=`
`(20)/(5)`

`x=4`

substitute the value gotten for x into equation 1 and 2

`men = 3x= 3(4)=12\\women=2x=2(4)=8`