Question

If the ratio of girls to boys on the trackteam is 5 to 6, which of these showspossible numbers of girls to boys onthe track team?A 24 girls, 20 boysB 50 girls, 56 boysC 60 girls, 50 boysD 20 girls, 24 boys

Answer 1

The ratio of 5 to 6 means that for every 5 girls on the track team there are 6 boys.

So, if there are n groups of 5 girls, there should be also n groups of 6 boys. Thus, we have the proportion:

`\frac{\text{ number of girls}}{\text{ number of boys}}=(5)/(6)`

Then, let's check each item to find out which one shows possible numbers of girls to boys on the track team.

A. 24 girls, 20 boys

`\frac{\text{ number of girls}}{\text{ number of boys}}=(24)/(20)=(24\colon4)/(20\colon4)=(6)/(5)\\e(5)/(6)`

B. 50 girls, 56 boys

`\frac{\text{ number of girls}}{\text{ number of boys}}=(50)/(56)=(50\colon10)/(56\colon10)=(5)/(5.6)\\e(5)/(6)`

C. 60 girls, 50 boys

`\frac{\text{ number of girls}}{\text{ number of boys}}=(60)/(50)=(60\colon10)/(50\colon10)=(6)/(5)\\e(5)/(6)`

D. 20 girls, 24 boys

`\frac{\text{ number of girls}}{\text{ number of boys}}=(20)/(24)=(20\colon4)/(24\colon4)=(5)/(6)`

Therefore, option D is correct.