Respuesta :
Let x be the number of children and let y be the number of adults.
We know that the total number of attendants was 147, then:
[tex]x+y=147[/tex]We also know that each child ticket cost $4 and for each adult cost $12, and the total amount collected were $1156. Then we have:
[tex]4x+12y=1156[/tex]Hence we have the system:
[tex]\begin{gathered} x+y=147 \\ 4x+12y=1156 \end{gathered}[/tex]Now we have to solve the system. To do that we solve the first equation for y:
[tex]y=147-x[/tex]and we plug this value into the second equation and solve for x:
[tex]\begin{gathered} 4x+12(147-x)=1156 \\ 4x+1764-12x=1156 \\ -8x=1156-1764 \\ -8x=-608 \\ x=\frac{-608}{-8} \\ x=76 \end{gathered}[/tex]Now that we have the value we can find the value of y, then:
[tex]\begin{gathered} y=147-76 \\ y=71 \end{gathered}[/tex]Therefore there were 76 children and 71 adults.
