Question

Suppose a theater sells adult tickets for a Shakespearean play for $18.00 each, and children's tickets for $10.00 each The receipts for one evening total $960.00 Ir 64 tickets were sold, how many were adult tickets?

Answer 1

We know that

• Adult tickets cost $18.00 each.

,

• Children's tickets cost $10.00 each.

,

• The total is $960.00.

,

• There were sold 64 tickets.

First, we define the equation for the total money earned one evening.

`18x+10y=960`

Where x is adult tickets, and y is children's tickets.

Now, we defined the equation for the total number of tickets.

`x+y=64`

We isolate x in the second equation.

`x=64-y`

Then, we replace this last equation in the first one to solve for y.

`\begin{gathered} 18(64-y)+10y=960 \\ 1152-18y+10y=960 \\ -8y=960-1152 \\ -8y=-192 \\ y=(-192)/(-8) \\ y=24 \end{gathered}`

There were sold 24 children tickets.

Now we find the number of adult tickets.

`\begin{gathered} x+24=64 \\ x=64-24 \\ x=40 \end{gathered}`

Therefore, there were sold 40 adult tickets.