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 .

Step-by-step explanation:

Since we have given that

Number of boys and girls = 32

Fraction of boys are going on a field trip = $\dfrac{2}{3}$

Fraction of girls are going on a field trip = $\dfrac{3}{4}$

Number of children left = 9

Let the number of boys be 'b'.

Let the number of girls be 'g'.

According to question, it becomes ,

$b+g=32------------(1)\\\\32-9=\dfrac{2}{3}b+\dfrac{3}{4}g\\\\23=\dfrac{2b}{3}+\dfrac{3g}{4}-------------(2)$

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

So, it becomes,

$\dfrac{2}{3}b+\dfrac{3}{4}(32-b)=23\\\\\dfrac{2}{3}b+24-\dfrac{3}{4}b=23\\\\\dfrac{2}{3}b-\dfrac{3}{4}b=23-24=-1\\\\\dfrac{8b-9b}{12}=-1\\\\\dfrac{-b}{12}=-1\\\\b=-1\times -12\\\\b=12$

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 .