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

Women = 3c + 5
Men = 4w - 3
 
w + m + c = 2838
3c + 5 + 4(3c+5) - 3 + c = 2838
3c + 5 + 12c + 20 - 3 + c = 2838
16c + 22 = 2838
16c = 2816
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

2129 + 533 + 176 = 2838