In a school of x students, 36 are in the honors program, and x% 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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