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A Broadway musical was attended by a total of 2,838 people, including men, women, and children. The number of women who attended the event was 5 more than 3 times the number of children, while the number of men was 3 less than 4 times the number of women. Write an equation to model this situation. Then, use the equation to find the number of men, women, and children who attended the musical.

Verified Answer :

texaschic101

m + w + c = 2838
w = 3c + 5
m = 4w - 3...4(3c + 5) - 3

4(3c + 5) - 3 + 3c + 5 + c = 2838
12c + 20 - 3 + 3c + 5 + c = 2838
16c + 22 = 2838
16c = 2838 - 22
16c = 2816
c = 2816/16
c = 176

w = 3c + 5
w = 3(176) + 5
w = 528 + 5
w = 533

m = 4w - 3
m = 4(533) - 3
m = 2132 - 3
m = 2129

check...
m + w + c = 2838
2129 + 533 + 176 = 2838
2838 = 2838 (correct)

men attending (m) = 2129
women attending (w) = 533
children attending (c) = 176

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