Question

At a movie theater the price of two adult tickets and six children is $54. The price of seven adult tickets and three children tickets is $81. What is the ticket price for one adult and one child ticket

Answer 1

Adult's ticket is $9

Children's ticket is $6

Explanation:

let A be the adult's ticket and C be the children's ticket

2A + 6C = 54 equation1

7A + 3C = 81 equation2

multiply equation2 by -2

-2(7A + 3C = 81)

-14A - 6C = - 162 equation3

add equations 1 and 3

2A + 6C = 54

-14A - 6C = - 162

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-12A = - 108

divide both sides by -12

A = $9

substitute A = 9 to any of the equations, i'll use equation1

2A + 6C = 54

2(9) + 6C = 54

18 + 6C = 54

6C = 36

C = $6