Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $15. For one performance,there were 50 tickets sold in all, and the total amount paid for them was $1275. How many tickets of each type were sold?

Answer 1

Given:

there are two types of tickets to a show: advance and same-day

Let the number of tickets from the type of Advance = x

And the number of tickets from the type of Same-day = y

there were 50 tickets sold in all

So,

`x+y=50\rightarrow(1)`

Advance tickets cost $30 and same-day tickets cost $15.

the total amount paid for them was $1275

So,

`30x+15y=1275\rightarrow(2)`

Solve the equations (1) and (2) to find (x) and (y)

`\begin{gathered} x+y=50\rightarrow(*-15) \\ 30x+15y=1275 \\ ============= \\ -15x-15y=-750 \\ 30x+15y=1275 \\ ============= \\ 15x=525 \\ x=(525)/(15)=35 \\ y=50-x=50-35=15 \end{gathered}`

So, The answer will be:

The number of tickets from the type of Advance = x = 35

And the number of tickets from the type of Same-day = y = 15