
Donald S. answered 06/02/16
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New to Wyzant
14-year math and science tutor
letting M=Men, W=Women, and C=Children, we know that
M+W+C=100
M=2W-4
M+W+6=C.
We want to add equations together such that we either solve for a variable numerically or in terms of the other variables. Let's take the first and third equations - they both contain the same variables. First, we'll rewrite the third equation so that it's in the same form as the first equation.
M+W+C=100
M+W-C=-6
Now, we multiply or divide the equations by a constant so that one or more of the variables cancel out when we the two equations together. If we multiply the first one by a constant of -1, both the M and W will cancel out when we add them.
-1(M+W+C=100)
M+W-C=-6
becomes
-M-W-C=-100
M+W-C=-6
adding the two equations together we get
0M+0W-2C=-106
rewritten it's
-2C=-106.
Now we solve for C by dividing both sides by -2, noting we get a positive answer when we divide a negative by a negative.
C=53
So, there were 53 children at this family gathering.