Question

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 reciept for admission totaled to $865.25. how many children and how many adults swam at the public pool that day??

SOLVE USING ELIMINATION
PLEASE SHOW ALL STEPS

Answer 1

Answer: x = 217 children swam
y = 264 adults swam

Step-by-step explanation:

Let:

1. x be the number of children who swam

2. y be the number of adults who swam

From the problem, we have the following system of equations:

x + y = 481 (equation 1)

1.25x + 2.25y = 865.25 (equation 2)

To eliminate x, we can multiply equation 1 by -1.25 and add it to equation 2:

-1.25x - 1.25y = -601.25

1.25x + 2.25y = 865.25

0.00x + 1.00y = 264

So, y = 264. This means that there were 264 adults who swam.

Substituting y = 264 into equation 1, we have:

x + 264 = 481

Solving for x, we get:

x = 481 - 264 = 217

Therefore, there were 217 children who swam.

So, the solution is:

x = 217 children swam

y = 264 adults swam

To check, we can substitute these values back into equation 2 and verify that the total admission price is $865.25:

1.25(217) + 2.25(264) = 865.25

So the solution is correct.

Answer 2

Answer: Therefore, 217 children and 264 adults swam at the public pool that day.

Step-by-step explanation: Let's use the elimination method to solve the problem.

Let's start by defining our variables:

c = number of children

a = number of adults

We know that the total number of people who used the pool is 481, so we can write the equation:

c + a = 481 (Equation 1)

We also know that the total admission receipts were $865.25, and that children pay $1.25 and adults pay $2.25, so we can write the equation:

1.25c + 2.25a = 865.25 (Equation 2)

To eliminate c from the equations, we can multiply Equation 1 by -1.25 and add it to Equation 2:

-1.25c - 1.25a = -601.25 (multiplying Equation 1 by -1.25)

1.25c + 2.25a = 865.25 (Equation 2)

0.00c + 1.00a = 264.00

Now we have an equation for a:

a = 264

We can substitute this value of a into Equation 1 to solve for c:

c + 264 = 481

c = 481 - 264

c = 217