There are 7891 people at a concert.1/3 of the adults are men.1/2 of the children are girls.The number of women is thrice the number of boys.How many children?

Question

Pls help me answer~

Answer 1

let x=# of adults

let y=# of children

x+y=7891

(1/3)x+(2/3)x+(1/2)y+(1/2)y=7891

The number of women, which is (2/3)x, is 3 times the number of boys.

(2/3)x=3(1/2)y

(2/3)x=(3/2)y

x/y=(3/2)/(2/3)

x/y=(9/4)

There are 9 adults for every 4 children.

9n+4n=7891

13n=7891

n=7891/13

n=607

9*607=5463 adults

4*607=2428 children is the answer

check: there are (2/3)*5463 women, or 3642 women

          there are 1214 boys

          3642=3*1214