Two adult tickets and 3 student tickets cost $12. One adult ticket and 2 students tickets cost $7. How much does each ticket cost.

Question

Write two equations then solve.

Answer 1

First let's let the variable a represent the cost of one adult ticket and the variable s represent the cost of one student ticket.

Using the information given, we can write the following equations:

2a + 3s = 12

1a + 2s = 7

Now we can solve these two equations with two unknowns using elimination by multiplying the second equation by -2 to eliminate the variable a and solve for s first:

2a + 3s = 12

-2a - 4s = -14

-1s = -2

s = 2

The cost of one student ticket will be $1.

To determine the cost of an adult ticket, substitute $1 for s in either of the original equations. Let's use the first equation:

2a + 3s = 12

2a + 3*2 = 12

2a + 6 = 12

2a +6 - 6 = 12 - 6

2a = 6

2a/2 = 6/2

a = 3

a= $3 The cost of one adult ticket will be $3 .