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?

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 = 437.50Equation 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