Question

Neptune Belvor decides to have a holiday festival at Convention Hall. There will be food and drinks for all, hotchocolate station, build your own gingerbread home competition, tree decoration station, make your ownholiday candle station and too top it all of SANTA will be there (or Coach IKE, dressed like him, real one is too busy).Tickets are selling for Students $5(under 18) and for Adults $11 (18+). The Event sold 9536 tickets and made$56,878. How many Adult tickets and how many Student tickets were sold?

Answer 1

Let 'x' represent the number of students tickets.

Let 'y' represent the number of adults tickets.

Two equations will be formed from the statements.

We were told that the total number of tickets sold is 9536 tickets.

`x+y=9536\ldots\ldots\ldots1`

The total cost of the tickets is $56,878.

Given that tickets are selling for students $5(under 18) and for Adults $11(18+).

`5x+11y=56878\ldots\ldots\ldots\text{.}.2`

Let us now combine the two equations and solve for x and y using the substitution method.

`\begin{gathered} x+y=9536\ldots\ldots\ldots.1 \\ 5x+11y=56878\ldots\ldots\ldots.2 \end{gathered}`

Solving for x and y

Isolate x for x + y = 9536

x = 9536 - y

Substitute x = 9536 - y into equation 2

`\begin{gathered} \begin{bmatrix}5\mleft(9536-y\mright)+11y=56878\end{bmatrix} \\ \end{gathered}`

Simplify

`\begin{bmatrix}47680+6y=56878\end{bmatrix}`

Solve for y

`\begin{gathered} 6y=56878-47680 \\ 6y=9198 \\ y=(9198)/(6)=1533 \\ \therefore y=1533 \end{gathered}`

For x = 9536 - y

`\begin{gathered} \mathrm{Substitute\: }y=1533 \\ x=9536-1533 \\ x=8003 \end{gathered}`

The solution to the system of equations is,

`x=8003,y=1533`

Hence, the number of tickets sold are

`\begin{gathered} \text{Student}=8003\text{ tickets} \\ \text{Adult}=1533\text{ tickets} \end{gathered}`