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.

Step-by-step 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.

$\dfrac{x-3}{y}=\dfrac{3}{4}\\\\\Rightarrow\ 4(x-3)=3(y)\\\\\Rightarrow\ 4x-12=3y$  

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