Question

On a certain hot​ summer's day, 369 people used the public swimming pool. The daily prices are $ 1.25 for children and $ 2.50 for adults. The receipts for admission totaled $ 775.00 . How many children and how many adults swam at the public pool that​ day?

Answer 1

118 children and 251 adults swam at the public pool that day.

Explanation:

Given:

On a certain hot​ summer's day, 369 people used the public swimming pool. The daily prices are $ 1.25 for children and $ 2.50 for adults. The receipts for admission totaled $ 775.00.

Now, to find the number of children and adults swam at the public pool that day.

Let the number of children be
`x.`

And let the number of adults be
`y.`

So, total number of people used the swimming pool:

`x+y=369\\\\x=369-y\ \ \ .....(1)`

Now, the total price for admission:

`1.25(x)+2.50(y)=775`

Substituting the value of
`x` from equation (1) we get:

`1.25(369-y)+2.50(y)=775`

`461.25-1.25y+2.5y=775\\\\461.25+1.25y=775`

Subtracting both sides by 461.25 we get:

`1.25y=313.75`

Dividing both sides by 1.25 we get:

`y=251.`

The number of adults = 251.

Substituting the value of
`y` in equation (1) we get:

`x=369-y\\\\x=369-251\\\\x=118.`

The number of children = 118.

Therefore, 118 children and 251 adults swam at the public pool that day.