Elimination by adding

Question

You sold 100 tickets to a high school concert. Student tickets are $4 and general admission tickets are $6 for a total of $440. How many of each type of ticket did you sell?

Answer 1

Answer 2

100= s+ g

440 = 4s + 6g

Multiply 1st equation by negative 4.

-4(100=s+g)

-400=-4sz6g

Add this to the second equation

-400=-4sz6g

440 = 4s + 6g

40=2g

20=g

20 general admission tickets were sold.

Now plug 20 into the simplest equation in place of g.

100= a + 20

80=s

20 general admission tickets and 80 student tickets were sold.

Answer 3

Suppose the number of student tickets is x.

Then the number of general admission tickets will be (100 - x)

Multiply the number of each type of ticket with its price and then add to a total of 440.

4x + 6(100 - x) = 440

4x + 600 - 6x = 440

-2x + 600 = 440

-2x + 600 - 600 = 440 - 600

-2x = -160

Divide both sides of the equation by -2 to get the value of x

x = 80

Number of student tickets sold = 80

Number of general admission tickets sold = 20