Question

The Jones family went to a play and paid $74 for 2 adults and 2 children. The Tucker family went to the same play and paid $86 for 2 adults and 3 children. Enter the price of an adult ticket.

Answer 1

The answer is $25.

x - the price of an adult ticket
y - the price of a child ticket

The Jones paid $74 for 2 adults and 2 children: 2x + 2y = 74
The Tuckers paid $86 for 2 adults and 3 children: 2x + 3y = 86

This is the system of two equations:
2x + 2y = 74
2x + 3y = 86
____
Multiply the first one by (-1)
2x * (-1) + 2y * (-1) = 74 * (-1)
2x + 3y = 86
____
-2x - 2y = -74
2x + 3y = 86
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Sum the equations:
2x - 2x + 3y - 2y = 86 - 74
y = 12
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Substitute y in the first equation to find x:
2x + 2 * 12 = 74
2x + 24 = 74
2x = 74 - 24
2x = 50
x = 50/2
x = 25

So, the price of the adult ticket is $25 and the price of the child ticket is $12.