At a family gathering there are 100 people. There are 4 less than twice as many women as men and 6 more children as both combined. How many children are at th

Question

I have 5 questions so I will be posting for a minute.

Answer 1

Hey there Ryan! My best general tip for solving these problems is to write down all of the information as soon as you read it. The first sentence states that there are 100 people at the gathering, and the gathering is made up of men, women and children, so I started by writing 100=M+W+C. This equation is not solvable so let's keep reading for more relevant information. The second sentence says that there are 4 less than twice as many women as men. This sentence gives us a way to write the variable W, in terms of the variable M, so

W= 2M-4 where W stands for women and M stands for men. Now we can read the next part. There are 6 more children as both combined, so we need to add together the number of men and women and then add 6. When we set this equal to our variable C we get C=M+W+6, and from the previous part of the problem we know that W=2M-4 so C=M+2M-4+6. Now we can take all 3 of our variables and put them back into the original equation and we get 100 = M+2M-4+2M-4+6. Now we can use algebra to solve for M. Combine like terms and you get that 100 = 6M-2. You add 2 to both sides and get 102=6M. Then divide 102 by 6 and M=17, but we aren't done! We have to take that value and substitute it back into the equation for C because the question is asking how many children are at the gathering. Recall that C=M+2M-4+6, which gives us that C=17+2(17)-4+6 which gives us that there are 53 children at the family gathering. I hope this helps!