Let a and c represent, respectively, the price of an adult and a child ticket. We know that
[tex]\begin{cases}3a+2c=78.94\\2a+3c=75.86\end{cases}[/tex]
Multiply the first equation by 3 and the second equation by 2 to get
[tex]\begin{cases}9a+6c=236.82\\4a+6c=151.72\end{cases}[/tex]
Subtract the two equations to have
[tex]5a=85.1 \iff a=17.02[/tex]
Plug this value in the first equation to get
[tex]3\cdot 17.02+2c=78.94\iff 2c=27.88\iff c=13.94[/tex]
