Question

Two adult tickets and 3 student tickets for a play cost $12. One adult ticket and 2 student tickets cost $7. How much is a student ticket?

Answer 1

Given:

The cost of 2 adult tickets and 3 student tickets = $12.

The cost of 1 adult ticket and 2 student tickets = $7.

Aim:

We need to find the cost of a student ticket.

Step-by-step explanation:

Let x be the cost of an adult's ticket.

Let y be the cost of a student's ticket.

Consider that the cost of 1 adult ticket and 2 student tickets is $7.

The equation for this statement is

`x+2y=7`

Substract 2y from both sides of the equation.

`x+2y-2y=7-2y`

`x=7-2y`

Consider that the cost of 2 adult tickets and 3 student tickets is $12.

The equation for this statement is

`2x+3y=12`

`\text{ Substitute }x=7-2y\text{ in the equation to find the value of y.}`

`2(7-2y)+3y=12`

`14-4y+3y=12`

`14-y=12`

Solve for y.

`14-12=y`
`y=2`

Final answer:

The cost of a student ticket = $2.