Question

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.

Answer 1

m + w + c = 2838
w = 3c + 5
m = 4(3c + 5) - 3 = 12c + 20 - 3 = 12c + 17

now we do some subbing
(12c + 17) + (3c + 5) + c = 2838...combine like terms
16c + 22 = 2838
16c = 2838 - 22
16c = 2816
c = 2816/16
c = 176 <== children

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

m = 12c + 17
m = 12(176) + 17
m = 2112 + 17
m = 2129 <=== men