At a certain college, there are 7 men for every 5 women. If there are 440 more men than women, what is the total enrollment?
Stephanie/Christina -- use a proportion as I showed you for the last problem.
I'll be glad to check your answer.
To find the total enrollment, we need to determine the number of men and women separately and then add them together.
Let's denote the number of men as "m" and the number of women as "w."
We are given two pieces of information:
1) At the college, there are 7 men for every 5 women, so the ratio of men to women is 7:5.
2) There are 440 more men than women.
From the first piece of information, we can set up the following equation:
m/w = 7/5
To solve for m and w, we need another equation. From the second piece of information, we can conclude that:
m = w + 440
Now we have two equations:
1) m/w = 7/5
2) m = w + 440
To solve this system of equations, we can substitute equation 2) into equation 1):
(w + 440)/w = 7/5
Next, cross-multiply to get rid of the fractions:
5(w + 440) = 7w
Simplify the equation:
5w + 2200 = 7w
Subtract 5w from both sides:
2200 = 2w
Divide both sides by 2:
w = 1100
Now that we have the value of w, we can substitute it back into equation 2) to find m:
m = w + 440
m = 1100 + 440
m = 1540
Finally, we find the total enrollment by adding the number of men and women together:
Total enrollment = m + w
Total enrollment = 1540 + 1100
Total enrollment = 2640
Therefore, the total enrollment at the college is 2640.