macattack wrote:How can we solve this question algebraically without plugging in the values:
1. The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were
added to the school, the new ratio of boys to girls would be 4 to 9. How many boys
currently attend the school?
(A) 27
(B) 48
(C) 54
(D) 72
(E) 108
Let x = the MULTIPLIER for the original ratio.
Original ratio of boys to girls is 2 to 5:
b/g = 2x/5x.
12 boys are added:
New b = 2x + 12.
New ratio of boys to girls is 4 to 9:
(2x + 12)/5x = 4/9.
Solving for x, we get:
18x + 108 = 20x
108 = 2x
x = 54.
Thus, the original number of boys = 2x = 2*54 = 108.
The correct answer is
E.
An alternate approach is to plug in the answers, which represent the original number of boys.
Since original b/g = 2/5, the original number of boys must be EVEN.
Eliminate A.
The remaining answer choices imply the following options for the original number of boys and girls:
B: b=24*
2=48, g=24*
5=120
C: b=27*
2=54, g=27*
5=135
D: b=36*
2=72, g=36*
5=180
E: b=54*
2=108, g=54*
5=270.
Since the addition of 12 boys will yield a new ratio of 4 to 9, and the number of girls does not change, the original number of girls must be a MULTIPLE OF 9.
Eliminate B, since 120 is not a multiple of 9.
After 12 boys are added to the remaining answer choices, we get:
C: b=66, g=135
D: b=84, g=180
E: b=120, g=270.
Only
E yields the required ratio of 4/9:
b/g = 120/270 = 4/9.
The correct answer is
E.
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