According to the given information, the equation that can be used to represent the escenario are:
[tex]\begin{gathered} x+y=57 \\ 6x+2.5y=265 \end{gathered}[/tex]
This is because x and y represent the number of adults and child tickets respectively, since 57 tickets were sold, the sum of x and y is 57.
Also, the sum of the cost of each ticket times the number of tickets sold is 265.
To find how many tickets were sold, we have to solve the system of equations and find x. We can use equalization method to solve it:
[tex]\begin{gathered} y=57-x \\ y=\frac{265-6x}{2.5} \end{gathered}[/tex][tex]\begin{gathered} 57-x=\frac{265-6x}{2.5} \\ 2.5(57-x)=265-6x \\ 142.5-2.5x=265-6x \\ 6x-2.5x=265-142.5 \\ 3.5x=122.5 \\ x=\frac{122.5}{3.5} \\ x=35 \end{gathered}[/tex]
35 adult tickets where sold.
