stne wrote:

SajjadAhmad wrote:

At Perry High School, the ratio of students who participate in either the band program or the choral program to students who participate in neither program is 3 to 8. If 220 students attend Perry High School, how many of them do NOT participate in either program?

(A) 40

(B) 60

(C) 100

(D) 160

(E) 180

Not able to grasp this.

Can anybody explain this a little bit more ?

Thank you.

stne , I'm not sure which part is unclear.

This question is a little bit about sets (who belongs to which group), but mostly about ratios (what portion of students belong to a group versus what portion of students do not belong to that group).

There are students who participate in either band or choir. Think of them as "participants." Call them P

Then there are students who are in neither program: they are in neither band nor choir. These are non-participants. Call them N

The ratio of students of who participate, to students who do not participate, is 3 to 8.

3P : 8N or 3x : 8x

Those are the parts of the ratio. You have to find the total of the parts:

(3 + 8) = 11.

If you grouped these students into bundles of 11, in every group of 11 students, 3 would be participants (P), and 8 would be non-participants (N).

There are 220 students. How many students, of those 220, do not participate (in either program)? A couple ways to solve.

1) Use a multiplier.

The ratio is 3x:8x = 11x

There are 220 students

11x = 220

x = 20 (multiplier)

8x students do not participate

So (8)(20) = 160 students do not participate (out of 220 students)

2) Use the ratio and make a fraction

3x : 8x = 11x. With this method, you can forget the x. The numbers in the ratio are what matter. There are two "wholes" to consider.

First is the "whole" of the ratio parts, which is 11:

N = \(\frac{part}{whole} =\frac{8}{11}\)

So \(\frac{8}{11}\) of the students do not participate (N).

The second "whole" to be used is total number of students at the school.

To find N, take \(\frac{8}{11}\) of

220.

\(\frac{8}{11}\) * 220 = 160 N students

160 students participate in neither band nor choir

Answer D

Hope that helps.