Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio of men to women?
(A) 5:2
(B) 5:1
(C) 4:3
(D) 4:1
(E) 3:1
[spoiler]OA=A[/spoiler]
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Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was
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Let F = number of Female and M = number of Male, we want to know the ratio of Male to Female $$\frac{M}{F}$$ or M: F
Formula: $$Average\ =\ \frac{sum\ of\ terms}{number\ of\ terms}$$
Solution: $$180\ =\ \frac{170\ F\ +\ 184\ M}{F\ +\ M}$$
Mulitple (F+M) on both side: $$180\ F\ +\ 180M\ =\ 170\ F\ +\ 184M$$
Subtract 180M and 170F: $$4M\ =\ 10\ F$$
Divide F and 4 on both side and simplify: $$\frac{M}{F}=\frac{5}{2}$$
Answer: A
Formula: $$Average\ =\ \frac{sum\ of\ terms}{number\ of\ terms}$$
Solution: $$180\ =\ \frac{170\ F\ +\ 184\ M}{F\ +\ M}$$
Mulitple (F+M) on both side: $$180\ F\ +\ 180M\ =\ 170\ F\ +\ 184M$$
Subtract 180M and 170F: $$4M\ =\ 10\ F$$
Divide F and 4 on both side and simplify: $$\frac{M}{F}=\frac{5}{2}$$
Answer: A
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Jay@ManhattanReview
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For the ratio purpose, say the no. of men is x and the no. of women is 1. So, we have to find out the value of x : 1.
Given the information, we have 180*( x + 1) = 184*x + 170*1
=> x = 5/2
The required ratio = x : 1 => 5/2 ; 1 => 5 : 2.
The correct answer: A
Hope this helps!
-Jay
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Solution:
We can create the following weighted average equation in which m = the number of men and w = the number of women. We need to determine m/w.
180 = (184m + 170w) / (m + w)
180m + 180w = 184m + 170w
10w = 4m
5w = 2m
5/2 = m/w
Answer: A
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