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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 89.ThatsameweekonTuesday,32childrenand25adultscametothepool,whichbroughtin89. 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?

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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 1andforadultsis1 and for adults is 2.

This problem has been solved

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