2012-03-26 09:00:30

At a certain party, the ratio of girl guests to boy guests is 2:3. If 10 boys left, then the ratio would be reversed. How many boys are at the party right now?

(A) 8
(B) 12
(C) 18
(D) 20
(E) 30

The correct answer is C

Explanation: Set up two proportions, one for the current ratio of boys to girls and one for the hypothetical ratio. Let b = the number of boys at the party and g = the number of girls. Thus, in its current form,

g/b = ⅔

And in its hypothetical form, in which the number of girls stays the same but the number of boys decreases by 10, the ratio is

g/(b - 10) = 3/2  (the "reversed" ratio of 2:3 is 3:2)

Cross multiply each of these to get

2b = 3g     &     3(b - 10) = 2g or 3b - 30 = 2g

Solve the 2b = 3g equation for g by dividing both sides of the equation by 3 to get g = ⅔b Now, substitute this value in for g in the second equation:

3b - 30 = 2(⅔b)

This simplifies to 3b - 30 = 1⅓b . Subtract 3b from both sides to isolate the variables. This leaves

-30 = -1⅔b

Divide both sides by - 1⅔  to get b = 18, making choice C correct.