Find the price of a senior citizen ticket and the price of a child ticket.

Question

Dan and Barry are selling cheesecakes and pizzas for a school fundraiser. Dan sold 8 cheesecakes and 6 pizzas for a total of $184. Barry sold 10 cheesecakes and 3 pizzas for a total of $140. What is the cost of 1 cheesecake and 1 pizza?

Answer 1

8c +6p =184

divide by 2

4c +3p = 92

10c +3p = 140

subtract

10c-4c = 140-92

6c = 48

c = $8 for 1 cheese steak

3p = 92-4c =92-32 = 60

p = $20 for 1 pizza

1 pizza and 1 cheese steak cost 20+8 = $28

Answer 2

C = price of C

P = price of P

8C + 6P = 184

10C + 3P = 140

Multiply 2nd equation by 2 and subtract from 1st equation

8C + 6P = 184

-(20C + 6P = 280)

-12C = -96

C = 8

plug C = 8 into first equation and solve for P:

8(8) + 6P + 184

64 + 6P = 184

6P = 120

P = 6

Price of pizzas are $6 each and price of cheesecakes are $8 each.