need to find how many adults and children to see show and write an equation

Question

adult tickets to play cost $22. TIckets for children cost $15. TIckets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group

Answer 1

x = number of adults

y = number of children

 

price for the group = (cost of adult seat)(number of adults) + (cost of children's seat)(number of children)

 

228 = 22x + 15y

 

but we know that 11 people attended.
So if x is the number of adults, then 11-x is the number of children

 

228 = 22x + 15(11-x)
228 = 22x +165 - 15x

228 = 7x + 165

63 = 7x

x = 9

9 adults in group

 

y = 11-x

y = 11-9 = 2

2 children in group

 

 

 

Answer 2

adult a = 22

children c = 15

 

a+c=11

 

22a + 15c = 228

 

22(11-c) +15c = 228

 

242 - 22c  +15c = 228

 

242 - 7c  = 228

c= 2 , a = 9