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?

1 Answer
Aug 6, 2015

Answer:

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#.