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?
Let x = multiplier. Thus,
Men = 7x
Women = 5x
The ratio of men to women is still 7 to 5.
Since there are 440 more men than women, we can say that
7x = 5x + 440
Solving for x,
7x - 5x = 440
2x = 440
x = 220
The total men and women is 7x + 5x = 12x. Thus the total is,
total = 12x
total = 12(220)
total = 2640
hope this helps :3
Well, according to the given information, there are 7 men for every 5 women. So, let's imagine we have a bunch of men standing in a line, and right next to them, we have some women also standing in a line.
Now, let's assume there are "x" men and "y" women. We know that for every 5 women, we have 7 men. So, we can write an equation as 7x = 5y. (Note: we are assuming that both x and y are whole numbers.)
Now, let's move on to the second part of the question. It says that there are 440 more men than women. So, we can write another equation as x = y + 440.
Now, we have a system of equations 7x = 5y and x = y + 440. We can solve these equations simultaneously to find the values of x and y.
But wait! You didn't ask me to solve the equations, you asked for the total enrollment. Silly me! To find the total enrollment, we need to add up the number of men and women.
So, the total enrollment would be x (the number of men) + y (the number of women). And that's your answer!
Let's assume the number of women at the college is x.
Since there are 7 men for every 5 women, the number of men would be (7/5) * x.
According to the given information, there are 440 more men than women, so we can write the equation as:
(7/5) * x - x = 440
To solve the equation, we can simplify it:
(7/5 - 1) * x = 440
(7/5 - 5/5) * x = 440
(2/5) * x = 440
To isolate x, we can multiply both sides by the reciprocal of (2/5), which is 5/2:
x = 440 * (5/2)
x = 1100
So, there are 1100 women at the college.
To find the total enrollment, we add the number of men and women together:
Total enrollment = (7/5) * x + x
Total enrollment = (7/5 * 1100) + 1100
Total enrollment = 7700/5 + 1100
Total enrollment = 1540 + 1100
Total enrollment = 2640
Therefore, the total enrollment at the college is 2640.
To solve this problem, we can set up a system of equations. Let's use the variable "m" to represent the number of men and "w" to represent the number of women.
From the given information, we know that there are 7 men for every 5 women. This can be written as:
m/w = 7/5 Equation 1
We are also given that there are 440 more men than women:
m = w + 440 Equation 2
Now, to find the total enrollment, we need to find the sum of the number of men and the number of women, which is m + w.
To solve the system of equations, we can substitute Equation 2 into Equation 1, since both equations are in terms of "m":
(w + 440)/w = 7/5
Now, we can solve this equation to find the value of "w":
Cross-multiplying, we get:
5(w + 440) = 7w
Expanding, we have:
5w + 2200 = 7w
Subtracting 5w from both sides, we have:
2200 = 7w - 5w
Simplifying, we get:
2200 = 2w
Dividing both sides by 2, we have:
w = 1100
Now that we know the value of "w", we can substitute it back into Equation 2 to find the value of "m":
m = 1100 + 440
m = 1540
Finally, to find the total enrollment, we add the number of men and the number of women:
Total enrollment = m + w
Total enrollment = 1540 + 1100
Total enrollment = 2640
Therefore, the total enrollment of the college is 2640.