On a certain hot summer day, 481 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $865.25. How... On a certain hot summer day, 481 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $865.25. How many children and how many adults swam at the public pool that day?
Understand the Problem
The question is asking us to find the number of children and adults that swam at the public pool, given the total number of people that used the pool and the total receipts for admission. This can be solved using a system of linear equations.
Answer
217 children and 264 adults.
Answer for screen readers
217 children and 264 adults swam at the public pool that day.
Steps to Solve
- Define variables
Let $c$ be the number of children and $a$ be the number of adults.
- Set up the equations
We know that the total number of people is 481, so:
$c + a = 481$
We also know that the total receipts are $865.25, so:
$1.25c + 2.25a = 865.25$
- Solve the system of equations
We can solve for $c$ in the first equation:
$c = 481 - a$
Substitute this expression for $c$ into the second equation:
$1.25(481 - a) + 2.25a = 865.25$
- Simplify and solve for $a$
Expand and simplify the equation:
$601.25 - 1.25a + 2.25a = 865.25$
Combine like terms:
$1.00a = 865.25 - 601.25$
$a = 264$
- Solve for $c$
Substitute the value of $a$ back into the equation $c = 481 - a$:
$c = 481 - 264$
$c = 217$
- State the answer
Therefore, there were 217 children and 264 adults.
217 children and 264 adults swam at the public pool that day.
More Information
This problem is a classic example of a system of linear equations, which can be used to model various real-world scenarios. The key to solving these types of problems is to correctly identify the variables and establish the relationships between them in the form of equations.
Tips
A common mistake is setting up the equations incorrectly, for example, confusing the coefficients or the variables. Another common mistake involves errors made during the algebraic manipulation of the equations. It's important to double-check each step to minimize calculation mistakes.
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