Question

Your third-grade classroom has 32 boys and girls. Two-thirds of the boys and three-fourths of the girls are going on a field trip. There are 9 children left. What is the ratio of boys to girls in your class?

Draw diagrams to support your answer.

Answer 1

Answer: The ratio of boys to girls would be 3 : 5 .

Explanation:

Since we have given that

Number of boys and girls = 32

Fraction of boys are going on a field trip =
`(2)/(3)`

Fraction of girls are going on a field trip =
`(3)/(4)`

Number of children left = 9

Let the number of boys be 'b'.

Let the number of girls be 'g'.

According to question, it becomes ,

`b+g=32------------(1)\\\\32-9=(2)/(3)b+(3)/(4)g\\\\23=(2b)/(3)+(3g)/(4)-------------(2)`

From eq(1), we get that g = 32-b

So, it becomes,

`(2)/(3)b+(3)/(4)(32-b)=23\\\\(2)/(3)b+24-(3)/(4)b=23\\\\(2)/(3)b-(3)/(4)b=23-24=-1\\\\(8b-9b)/(12)=-1\\\\(-b)/(12)=-1\\\\b=-1* -12\\\\b=12`

so, number of girls would be 32 - b = 32 - 12 = 20

So, Ratio of boys to girls in class would be 12 : 20 = 3 : 5.

Therefore, the ratio of boys to girls would be 3 : 5 .