Question

There are two types of tickets sold at the Canadian Formula One Grand Prix race. The price of 6 grandstand tickets and 4 general admission tickets is $3200. The price of 8 grandstand tickets and 8 general admission tickets is $4880. What is the price of each type of ticket?

Answer 1

Let:

x = price of the grandstand ticket

y = price of the general admission ticket

The price of 6 grandstand tickets and 4 general admission tickets is $3200, so:

`6x+4y=3200`

The price of 8 grandstand tickets and 8 general admission tickets is $4880, so:

`8x+8y=4880`

Let:

`\begin{gathered} 6x+4y=3200_{\text{ }}(1) \\ 8x+8y=4880_{\text{ }}(2) \end{gathered}`

Using elimination method:

`\begin{gathered} 2(1)-(2)\colon_{} \\ 12x-8x+8y-8y=6400-4880 \\ 4x=1520 \\ x=(1520)/(4) \\ x=380 \end{gathered}`

replace the value of x into (1):

`\begin{gathered} 6(380)+4y=3200 \\ 2280+4y=3200 \\ 4y=3200-2280 \\ 4y=920 \\ y=(920)/(4) \\ y=230 \end{gathered}`

The price of the grandstand ticket is $380 and the price of the general admission ticket is $230