Question

Mike went to a football game with his family. They bought 5 boxes of popcorn and 3 programs, and spent $41. Sean's family went to the same game, bought 3 boxes of popcorn and 2 programs, and spent $26. How much does each program cost at the game? (1 point) $4 $5 $6 $7

Answer 1

Let the price of a box of popcorn = b and the price of a program = p
we can make 2 equations:
5b+3p = 41 and 3b+2p=26

We can use the subtraction method be able to eliminate one of the variables and isolate the other one - to do it I will equalize the 'b' in both equations by multiplying by 5 and 3 respectively

5(3b+2p=26)
-3(5b+3p = 41)

15b+10p=130
-(15b+9p=123)

p=7 (therefore the answer is 7$)

Answer 2

The cost of each program in the game, given the data is $7

Assumption

• Let b represent the number of box of popcorn
• Let p represent the number of program

Data obtained from the question

• First statement: 5b + 3p = 41
• Second statement: 3b + 2p = 26
• Cost of each program =?

How to determine the cost for each program

5b + 3p = 41 (1)

3b + 2p = 26 (2)

Make b the subject in equation (1)

5b + 3p = 41

5b = 41 - 3p

b = (41 - 3p) / 5 (3)

Substitute the value of b in equation (3) into equation (2)

3b + 2p = 26

3[(41 - 3p) / 5] + 2p = 26

(123 - 9p) / 5 + 2p = 26

Multiply through by 5

123 - 9p + 10p = 130

123 + p = 130

Collect like term

p = 130 - 123

p = $7

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