Respuesta :
We know that
• The ticket for children costs $21.
,• The ticket for adults costs $36.
,• There were 19 people.
,• The total gate revenue is $56,400.
To solve this we have to form a system of linear equations. The first equation would be
[tex]x+y=1,900[/tex]Where x is children and y is adults, there were 19 in total.
The second equation would be
[tex]21x+36y=56,400[/tex]This equation represents the total earnings.
Let's isolate y in the first equation.
[tex]y=1,900-x[/tex]Now, we replace this expression in the second equation.
[tex]\begin{gathered} 21x+36(1,900-x)=56,400 \\ 21x+68,400-36x=56,400 \\ -15x=56,400-68,400 \\ -15x=-12,000 \\ x=\frac{-12,000}{-15} \\ x=800 \end{gathered}[/tex]There were 800 children.
Then, we use this value to find y.
[tex]\begin{gathered} y=1,900-x \\ y=1,900-800 \\ y=1,100 \end{gathered}[/tex]