# 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?

Aug 6, 2015

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

$40 \cdot x + 35 \cdot y = 2425$

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

$\left\{\begin{matrix}x + y = 65 \\ 40 x + 35 y = 2424\end{matrix}\right.$

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 $y$

$40 \cdot \left(65 - y\right) + 35 y = 2425$

$2600 - 40 y + 35 y = 2425$

-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.