Question

The combined cost of one advance ticket to a show and one same-day ticket was $65. It is known that 40 tickets were sold in advance and 35 the same day, for total receipts of $2425 . What was the price of each kind of ticket?

Answer 1

Advance ticket: `$30`
Same-day ticket: `$35`

Explanation:

Let's say that the price of the advance ticket is `x` and the price of the same-day ticket is `y`.

You know that the combined cost of two tickets, one of each type, is `$65`. This will be your first equation

`x + y = 65`

Now, you know that you sold a total of `40` advance tickets and `35` same-day tickets for a total value of `$2425`. This will be your second equation

`40 * x + 35 * y = 2425`

Now you have a system of two equations with two unknowns.

`{(x+y = 65), (40x + 35y = 2424) :}`

Use the fist equation to write `x` as a function of `y`

`x+y = 65 implies x = 65 - y`

Now use this expression in the second equation to solve for `y`

`40 * (65 - y) + 35y = 2425`

`2600 - 40y + 35y = 2425`

`-5y = -175 implies y = 175/5 = color(green)($35)`

Now use this value of `y` to solve for the value of `x`

`x+y = 65 implies x = 65 - 35 = color(green)($30)`

Therefore, the price of an advanced ticket is `$30` and the price of a same-day ticket is `$35`.