Question

On a certain hot summer's day, 544 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $964.00. How

many children and how many adults swam at the public pool that day?

Answer 1

248 children

296 adults

Explanation:

Define the variables:

• Let x = number of children using the public pool.
• Let y = number of adults using the public pool.

Given information:

• A total of 544 people used the public swimming pool.
• The daily prices are $1.50 for children and $2.00 for adults.
• The receipts for admission totalled $964.00.

Create a system of equations with the given information and defined variables:

`\begin{cases}\;\;\;\;\:\:\:x+y=544\\1.5x+2y=964\end{cases}`

Rearrange the first equation to isolate x:

`\implies x=544-y`

Substitute the found expression for x into the second equation and solve for y:

`\implies 1.5(544-y)+2y=964`

`\implies 816-1.5y+2y=964`

`\implies 816+0.5y=964`

`\implies 0.5y=148`

`\implies y=296`

Therefore, 296 adults swam at the public pool.

Substitute the found value of y into the equation for x and solve for x:

`\implies x=544-296`

`\implies y=248`

Therefore, 248 children swam at the public pool.