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.

Total= 2838
x= # of children
3x+5= # of women
4(3x+5)-3= # of men

x + (3x+5) + 4(3x+5)-3= 2838
multiply 4 by 3x+5 first

x + (3x+5) + (4*3x) + (4*5) - 3= 2838
combine like terms

4x + 5 + 12x + 20 - 3= 2838
16x + 22= 2838
subtract 22 from both sides

16x= 2816
divide both sides by 16

x= 176

ANSWER:
# Children= x= 176
# Women= 3x+5= 3(176)+5= 533
# Men= 4(3x+5)-3=4(3(176)+5)-3= 2129

CHECK:
#children + #women + #men= 2838
176 + 533 + 2129= 2838
2838= 2838

Hope this helps! :)