Question

A drama club earns $1040 from a production. A total of 64 adult tickets and 132 student tickets were sold. An adult ticket costs twice the price of a student ticket. What is the price of each type of ticket?

Answer 1

Let's call the price of an adult ticket as A and the price a student ticket as S. From the first two sentences "A drama club earns $1040 from a production. A total of 64 adult tickets and 132 student tickets were sold." we know that the total amount earned was $1040, and this value was reached by selling 64 adult tickets and 132 student tickets. The amount earned selling adult tickets is given by the product between the unitary price of an adult ticket and the amount of adult tickets sold. The same logic goes to the amount earned selling student tickets. We know that the sum of those two quantities adds up to $1040, therefore, we have the following equation.

`64A+132S=1040`

From the other sentence, "An adult ticket costs twice the price of a student ticket. " we get a new relationship between A and S. A is equal to 2S.

`A=2S`

Now we have a system with two variables and two equations. If we substitute the second equation on the first one we get a new equation only for S.

`\begin{cases}64A+132S=1040 \\ A=2S\end{cases}\Rightarrow64(2S)+132S=1040`

Solving this equation for S, we have

`\begin{gathered} 64(2S)+132S=1040 \\ 128S+132S=1040 \\ (128+132)S=1040 \\ 260S=1040 \\ S=(1040)/(260) \\ S=4 \end{gathered}`

The student ticket price is $4.

Using this value for S, we can substitute in one of the equations to find the value for A.

`\begin{cases}A=2S \\ S=4\end{cases}\Rightarrow A=2(4)=8`

The price of the adult ticket is $8.