Question

Swimming Pool On a certain hot summer's day, 600 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled $1021.50. How many children and how many adults swam at the public pool that day? There were children at the public pool.

Answer 1

Given:

No of people - 600

Rate:

Children - $ 1.25

Adults - $ 2.00

Total Admission - $ 1,021.50

Required:

No. of children and adults that day

Solution:

Let x - be the number of children

y - be the number of adults

We can write the expression for the total number of people in the pool as:

`x+y=600`

And the expression for the total admission is:

`1.25x+2y=1021.5`

From the first equation we can write:

`x=600-y`

Now, we will substitute the expression for x into the second espression (for the total admission):

`\begin{gathered} 1,25x+2y=1021.5 \\ 1.25(600-y)+2y=1021.5 \\ 750-1,25y+2y=1021.5 \\ -1,25y+2y=1021.5-750 \\ 0.75y=271.5 \\ y=362 \end{gathered}`

If y = 362, then x is:

`x=600-y=600-362=238`

Answer:

There are 238 children and 362 adults in the pool that day.

To check:

Substiture the value of x and y into the second espression (for the total admission):

`\begin{gathered} 1,25x+2y=1021.5 \\ 1.25(238)+2(362)=1021.5 \\ 297.5+724=1021.5 \\ 1021.5=1021.5 \end{gathered}`

The computed value of x and y satisfies the second equation. Our answer is correct.