Question

The ratio of the number of men to the number of women was 5:9 at a museum. The ratio became 2:3 when 42 women left the museum. Find the total number of men and women at the museum at the beginning.​

Answer 1

150 men and 252 women

Explanation:

Ratio:

Men : Women = 5 : 9

Number of men = 5x

Number of women = 9x

42 women left the museum.

Number of remaining women = 9x - 42

New ratio = 2 : 3

`(5x)/(9x -42)=(2)/(3)\\\\\\\bf Cross \ multiply,`

3*5x = 2*(9x - 42)

15x = 2*9x - 2*42

15x = 18x - 84

18x - 84 = 15x

Add 84 to both the sides,

18x = 15x + 84

Subtract 15x from both sides,

18x - 15x = 84

3x = 84

Divide both sides by 3,

x = 84 ÷ 3

x = 28

Number of men = 5 * 28 = 140

Number of women = 9*28 = 252