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:
[tex]\begin{cases}x+y=527 \\ 1.75x+2.5y=1054.25\end{cases}[/tex]Using the substitution method we can clear y from the first equation:
[tex]\begin{gathered} x+y=527 \\ y=527-x \end{gathered}[/tex]Replace into the second equation:
[tex]\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}[/tex]And solving for x:
[tex]\begin{gathered} -0.75x=1054.25-1317.5 \\ -0.75x=-263.25 \\ x=\frac{-263.25}{-0.75}=351 \end{gathered}[/tex]Replacing x = 351 in the first equation we can find y:
[tex]y=527-x=527-351=176[/tex]Answer:
• Children: ,351
,• Adults: ,176
