In a school ofxstudents, 36 are in the honors program, andx%of the 35 female students are in the honors program. If 15 male students are in the honors program, what fraction of all the non-honors students are female?

(A) 5/12

(B) 7/12

(C) 6/15

(D) 7/15

(E) 8/15

Go to it! My answer will eventually appear in the comments.

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## 1 comment:

I did this somewhat hastily, so I admit I might be wrong, but I think the answer is (B), 7/12.

With all such problems, it's a good idea to list what you know, and also what you can immediately deduce from the givens. Here's what I scribbled:

x = total # students (given)

36 = total # honors students (given)

15 = total # male honors students (given)

21 = total # female honors students (deduced)

35 = total # female students (given)

x - 35 = total # male students (deduced)

The same "x" is used as a percentage: "x% of the 35 female students are in the honors program." Whatever that x% is, I already know the raw number of female honors students is 21, something I quickly deduced. So I can set up an equation:

(x/100)•35 = 21

When I solve for x, I get

x = 60, which is the total number of students. From this, we deduce

60 - 36 = 24 = total # non-honors students

35 - 21 = 14 = total # female non-honors students

14/24 = 7/12 = the looked-for ratio

Therefore (B).

Did I do this right?

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