How many of each type of ticket were sold?

Question

The senior class all 245 tickets to the class play. Theater tickets sold for four dollars each and listing student tickets for $2.50 each. The total income from the ticket sales for $725. How many of each type of ticket were sold?

Answer 1

Let x = number of theater tickets sold, each being $4 each

Let y = number of student tickets sold, each being $2.50 each

The total number of tickets is x+y = 245

The total income will be 4x + 2.50y = 725

Set up the two following equations,

x+y = 245 ...1

4x+2.50y = 725 ...2

Multiply equation 1 by 4, 4x+4y = 980 ...3

Now lets subtract equation 3 by equation 2. With that, we get -1.5y = -255. After that, lets divide both sides by -1.5 which will get us to y=170, that being a total of 170 theater tickets sold.

The only thing we have left to figure is the number of student tickets. Plugging our solved y=170 to equation 1, x+170 = 245. That will get us to x = 245 - 170 = 75. That will total to 75 student tickets sold.

In short, there are 170 theater tickets sold and 75 student tickets sold.

Answer 2

T+S = 245

4T + 2.5S = 725

4T =4S = 980

subtract

4T + 2.5S = 725 to eliminate T

1.5S =255

S = 255/1.5 = 85/.5 = 170 student tickets

T=245-170 = 75 regular tickets