Question

on certain hot summers day , 527 people used the public swimming pool. the daily prices are 1.75 for children and 2.50 for adults. the receipt for admission totaled 1054.25. how many children and how many adults swam at the public pool that day?

Answer 1

Step-by-step explanation:

• x: number of ,children, that swam at the public pool

,

• y: number of ,adults, that swam at the public pool

We can write a system of linear equations:

`\begin{cases}x+y=527 \\ 1.75x+2.5y=1054.25\end{cases}`

Using the substitution method we can clear y from the first equation:

`\begin{gathered} x+y=527 \\ y=527-x \end{gathered}`

Replace into the second equation:

`\begin{gathered} 1.75x+2.5(527-x)=1054.25 \\ 1.75x+2.5\cdot527-2.5x=1054.25 \\ (1.75-2.5)x+1317.5=1054.25 \end{gathered}`

And solving for x:

`\begin{gathered} -0.75x=1054.25-1317.5 \\ -0.75x=-263.25 \\ x=(-263.25)/(-0.75)=351 \end{gathered}`

Replacing x = 351 in the first equation we can find y:

`y=527-x=527-351=176`

Answer:

• Children: ,351

,

• Adults: ,176