PSAT Math Grid-Ins Question 127: Answer and Explanation

Question: 127

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 are a total of 4,000 students,
m + w = 4,000. To solve this system of equations, solve the first equation for m. Then plug this value into the second equation using substitution. Solving for m gives:

So the second equation becomes:

Combine like terms:

Dividing by (the same as multiplying by ) tells you that
w = 2,400. To figure out how many more women there are than men, you need to know also how many men there are. Plug in 2,400 for w in the equation you already solved in terms of m. Then subtract the number of men from the number of women:


So there are 800 more women than men.