Question

The City Zoo has different admission prices for adults and children. When three adults and two children went to the​ zoo, the bill was​ $78.94. If two adults and three children got in for ​$75.86​, then what is the price of an adult's ticket and what is the price of a​ child's​ ticket?

Answer 1

Let a and c represent, respectively, the price of an adult and a child ticket. We know that

`\begin{cases}3a+2c=78.94\\2a+3c=75.86\end{cases}`

Multiply the first equation by 3 and the second equation by 2 to get

`\begin{cases}9a+6c=236.82\\4a+6c=151.72\end{cases}`

Subtract the two equations to have

`5a=85.1 \iff a=17.02`

Plug this value in the first equation to get

`3\cdot 17.02+2c=78.94\iff 2c=27.88\iff c=13.94`