Question 597144: ticket for a show cost $5 for the balcony seat and $12 for the orchestra seat.on sunday 300 ticket were sold for the amount of $2410.how many of each type of ticketa wee sold that day
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
This process works for "two kinds of ticket" problems and "two kinds of coins" problems.
Let  represent the number (as yet unknown) of one of the items. Let  represent the number of the other item.
The sum  is then equal to the total number of items (300 in this problem).
Each type of item has a value ) or ) per item. For your particular ticket problem, the value of each of the items is $5, while the value of each of the items is $12. In a coin problem, dimes are worth 10 cents, quarters 25 cents, and so on.
The value of all of the items is the value of one of them times the number of them, that is:  , while the value of the items is, similarly:  . The sum of these values is the total value given in the problem. For your problem, $2410.
From this information, you can create two equations (a necessary thing to be able to do because you have two variables, namely and ).
In general:
Specifically for your problem:
Given the simplicity of the first equation in these types of problems, I recommend that you use the substitution method to solve the 2X2 system of equations.
John
My calculator said it, I believe it, that settles it
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