If the ratio of boys to girls in the school band is 2 to 3, which of these show possible numbers of the boys and girls in band.

A. 24 boys, 36 girls
B. 20 boys, 35 girls
C. 36 boys, 24 girls
D. 35 boys, 20 girls

A

Step-by-step explanation:

Simply guess and check, meaning the boys category must be divisible by 2 and the girls category must be divisible by 3

A: 24 boys ÷ 2 = 12 (equals a whole number so it is divisible; not a decimal)

36 girls ÷ 3 = 12 (both of the boys and girls are divisible by their corresponding numbers)

Yes

Now make sure the boys are a lower count than the girls as the ratio says it should be 2 to 3, meaning there are more girls than boys

B: 20 ÷ 2 = 10 (divisible)

35 ÷ 3 = 11.666 (this is a decimal answer so it is not divisible)

No

C: 36 ÷ 2 = 18

24 ÷ 3 = 8

Yes, they are divisible

Now lets check if boys have a lower count than girls

36 boys > 24 girls

This is not the solution as it doesn't reflect the correct ratio of less boys than girls

D: 35 ÷ 2 = 17.5 (not divisible)

20 ÷ 3 = 6.66 (not divisible)

14

step-by-step explanation: