The Johnson family attends opening day at the tigers stadium for $165, buying two adult tickets and four child tickets. The Robison family also attended opening day and brought four adult tickets and three child tickets for $235. How much does an adult ticket cost and how much does a child ticket cost?

The answer is that adult tickets cost $44.50 and child tickets cost $19.

Step-by-step explanation:

Let c = the cost of child tickets and a = the cost of adult tickets.

The total amount is equal to the number of adult tickets time the cost of adult tickets plus the number of child tickets times the cost of child tickets. Set up two equations:

2a + 4c = 165

4a + 3c = 235

Solve the top equation for a:

2a + 4c = 165

2a = 165 - 4c

a = 165/2 - 4c/2

a = 82.5 - 2c

Substitute into the second equation:

4a + 3c = 235

4 (82.5 - 2c) + 3c = 235

330 - 8c + 3c = 235

-5c = - 95

c = - 95 / - 5 = 19, so child ticket cost $19.

Solve for a:

a = 82.50 - 2c

a = 82.50 - 2 (19)

a = 82.50 - 38

a = $44.50, so adult tickets cost $44.50.

Proof using the first equation for the Johnson family:

2a + 4c = 165

2 (44.50) + 4 (19) = 165

89 + 76 = 165

165 = 165

Proof using the second equation for the Robison family:

4a + 3c = 235

4 (44.50) + 3 (19) = 235

178 + 57 = 235

235 = 235