Digital PSAT Math Practice Question 224: Answer and Explanation
Question: 224
On a particular college campus, there are two men for every three women. If the total number of men and women on campus is equal to 4,000, how many more women are there on campus than men?
Correct Answer: 800
Explanation:
800 This is a system of equations. If there are 2 men for every 3 women, the ratio is 
. If there is a total of 4000 students, m + w = 4000. To solve this system of equations, solve the first equation for m and plug this into the second equation using substitution. Solving for m, you get 
, so the second equation becomes 
. Combine like terms: 
. Dividing by 
(the same as multiplying by 
) tells you that w = 2400. To figure out how many more women there are than men, you also need to know how many men there are. Plug 2400 in for w in the equation you already solved in terms of m:
w - m = 2400 - 1600 = 800, so there are 800 more women than men.
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