Question

On a certain hot summer's day, 263 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $437.50. How many children and how many adults swam at the public pool that day?

Answer 1

To find the number of children and adults who swam at the public pool, we can set up a system of equations using the information given. Solving this system will give us the desired values. There were 176 children and 87 adults who swam at the public pool that day.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's say the number of children be x and the number of adults be y. We can write two equations based on the information given:

1.25x + 2.5y = 437.5 (total receipts for admission)

x + y = 263 (total number of people)

We can solve this system of equations using any method, such as substitution or elimination. Let's use the elimination method by multiplying the second equation by 1.25 to make the coefficients of x in both equations the same:

1.25x + 1.25y = 328.75

1.25x + 2.5y = 437.5

Subtract the first equation from the second equation:

1.25y = 108.75

y = 87

Substitute this value of y back into the second equation to find x:

x + 87 = 263

x = 176

Therefore, there were 176 children and 87 adults who swam at the public pool that day.

Answer 2

The number of children = x = 176

The number of Adults = y = 87

Step-by-step explanation:

Let us represent

The number of children = x

The number of Adults = y

On a certain hot summer's day, 263 people used the public swimming pool.

x + y = 263.... Equation 1

x = 263 - y

The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $437.50.

$1.25 × x + $2.50 × y = $437.50

1.25x + 2.50y = 437.50.....Equation 2

We substitute 263 - y for x in Equation 2

1.25(263 - y) + 2.50y = 437.50

328.75 - 1.25y + 2.50y = 437.50

- 1.25y + 2.50y = 437.50 - 328.75

1.25y = 108.75

y = 108.75 ÷ 1.25

y = 87

Solving for x

x = 263 - y

x = 263 - 87

x = 176

Therefore:

The number of children = x = 176

The number of Adults = y = 87