Question

Blinn College in Bryan has 620 students. The difference between male students and female students is 20. How many female students are there?

Answer 1

320 men and 300 women

Explanation:

This problem is slightly unclear to me, because it does not say whether there are more boys than girls or more girls than boys, but it say the difference between men and women are 20 so I'm going to assume that there are more men than women.

There are two approaches to solving this problem. I'll show the easy way first:

There are 620 students total and the difference between men and women are 20, so all we have to do is simplify it. Take half of the total students which is 310. So 310 are male and 310 are female, but the difference between them is 20, so if we add 10 to the males and subtract 10 from the females the difference between them will be 20 and they'll still add to 620. so 310+10= 320 and 310-10=300. So there are 320 men and 300 women. Then just check your work by adding them together and you see that they add to 620.

The second way, which your teacher probably wants, is to do it algebraically. You are going to have to do this with more complicated scenarios in the future so I suggest doing it this way. Set up a system of equations with the information given. First we're solving for unknowns so lets make variables for the males and females. `m` = men and `w` = women. Here's what we know represented as functions:

`m-w=20` (Their difference is 20)
`m+w=620` (Their total is 620)

solve for `m` in the first equation:
`m=w+20`

substitute that for `m` in the second equation:

`(w+20) +w=620`

combine like terms:

`2w+20=620`
solve for `w` by subtracting 20 from both sides, then dividing both sides by 2:
`w=300`

then substitute that for `w` in either of the original equations and you get:

`m=320`

So there are 320 men and 300 women.