27 total people. 7 more men than women. How many women?

Answer 1

Hi! So to solve this question we can break it down into smaller parts.

First, we are given a total number of people (men and women): 27. We can turn this into an equation where m is the number of men and w is the number of women: m+w=27

Next it tells us that there are 7 more men than women. This means that what ever number of women there are, there are 7 more men. We can turn this into an equation where m is the number of men and w is the number of women. m=w+7 Lets rearrange this by subtracting w from each side to get: m-w=7. Now we can set up a system of equations:

m+w=27

m-w=7

Now we can simplify this system by first canceling out the number of men by multiplying the whole bottom row by -1:

m+w=27 m+w=27

-(m-w=7) = -m+w=-7

We can now add these two equations together to get: 2w=20 and divide both sides by 2 to get: w=10. We now know that there are 10 women and the problem tells us that there are 7 more men than women so m=10+7=17

Final Answer: 10 women and 17 men

Hope this helps!