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can soemone help me solve it through an equation?

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Senior | Next Rank: 100 Posts
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by r_walid » Tue Jan 27, 2009 6:47 pm
in a college, the ratio of faculty to students is 1:9.
if 2/3 students are female and 1/4 of faculty are female, what is the fraction of combined students and faculty are female?

The problem can be solved easily if you assume the total number os students and faculty and backsolve. but i tried to do it through an equation but i get stuck halfway through it. can someone solve this THROUGH an equation with variables instead of substituting the variables with assume numbers?

Thank you
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by gaggleofgirls » Tue Jan 27, 2009 7:33 pm
Here's the formula I used...

1:9 means that
1/10 of the total population is Faculty = f=t/10
9/10 of the total population is Students s = 9t/10

1/4 * t/10 = fraction of the Faculty that is female
2/3 * 9t/10 = fraction of Students that are female

combined means to add, so add them together to get the fraction of the total that is female :

1/4*t/10 + 1/3*9t/10

Solve for this and you get 5/8 of the total population is female.

-Carrie
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