Question

Solve the following problem first using a tape diagram and then using an equation: In a school choir, 1/2 of the members were girls. At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4. How many boys remained in the choir?

Answer 1

Answer: 9 boys remained in the choir.

Explanation:

Let x be the number of of boys and y be the number of girls.

In a school choir, 1/2(half) of the members were girls.

i.e
`x=y` (1)

At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4.

`(x-3)/(y)=(3)/(4)\\\\\Rightarrow\ 4(x-3)=3(y)\\\\\Rightarrow\ 4x-12=3y`

Put y= x from (1), we get

`4x-12=3x\\\\\Rightarrow\ 4x-3x=12\\\\\Rightarrow\ x=12`

Thus , the number of boys : x= 12

Boys remained in the choir = 12-3=9