The manager at a community pool is looking over receipts. On a certain Monday, the pool had 39 children and 25 adults, which brought in $89. That same week on Tuesday, 32 children and 25 adults came to the pool, which brought in $82. What are the admission prices for children and adults?
Question
The manager at a community pool is looking over receipts. On a certain Monday, the pool had 39 children and 25 adults, which brought in 82. What are the admission prices for children and adults?
Solution
To solve this problem, we can set up a system of linear equations based on the information given.
Let's denote the price of a child's ticket as C and the price of an adult's ticket as A.
From the information given for Monday, we can write the first equation as: 39C + 25A = 89
From the information given for Tuesday, we can write the second equation as: 32C + 25A = 82
Now we have a system of two equations, and we can solve it step by step.
First, let's subtract the second equation from the first one: (39C + 25A) - (32C + 25A) = 89 - 82 This simplifies to: 7C = 7 So, C = 1
Now that we know C = 1, we can substitute it into the first equation: 39*1 + 25A = 89 This simplifies to: 25A = 89 - 39 25A = 50 So, A = 50 / 25 = 2
Therefore, the admission price for children is 2.
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