Question

Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,783 was collected on the sale of 1,235 tickets. How many of each type of ticket were sold?
The basketball game sold_____adult tickets and___sudent tickets.

Answer 1

A = the number of adult tickets

S = the number of student tickets

[you can use different variables x, z, t, etc...]

5A + S = 2783        [$5 per adult plus $1 per student = total $2783]

A + S = 1235       [# of adults plus # of students = 1235]

To find A and S, you need to do substitution. First isolate one of the variables using either one of the equations, I will isolate the A in A + S = 1235:

A + S = 1235     Subtract S on both sides of the equation

A = 1235 - S

Next substitute/plug in (1235 - S) for A to find the value of S:

5A + S = 2783                        [isolate/get S by itself in the equation]

5(1235 - S) + S = 2783        Distribute/multiply 5 into (1235 - S)

(5)1235 - (5)S + S = 2783

6175 - 5S + S = 2783       Combine like terms  (-5s and S)

6175 - 4S = 2783             Subtract 6175 on both sides

-4S = -3392          Divide -4 on both sides

S = 848

Now that you found S, you can use it to find A:

A + S = 1235

A + 848 = 1235      Subtract 848 on both sides

A = 387

S = 848 student tickets

A = 387 adult tickets