Question

The ratio of the number of boys to the number of girls in a dance club is 5 : 6. After 6 more boys join the club, the ratio became 13 : 12. How many people were in the club at the start?

Answer 1

44

Explanation:

let boys be x and girls be y

x/y=5/6

x=5y/6....(1)

if 6 boys join the club that will be x+6

Therefore:

(x+6)/y=13/12

13y=12x+72

13y-12x=72

Recall x=5y/6

Therefore:

13y-12(5y/6)=72

13y-(2*5y)=72

13y-10y=72

3y=72

y=24 people

Therefore:

x=(5*24)/6

x=20 people

Therefore people in the club before are 20+24=44