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.
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
[tex]x+2y=7[/tex]Substract 2y from both sides of the equation.
[tex]x+2y-2y=7-2y[/tex][tex]x=7-2y[/tex]Consider that the cost of 2 adult tickets and 3 student tickets is $12.
The equation for this statement is
[tex]2x+3y=12[/tex][tex]\text{ Substitute }x=7-2y\text{ in the equation to find the value of y.}[/tex][tex]2(7-2y)+3y=12[/tex][tex]14-4y+3y=12[/tex][tex]14-y=12[/tex]Solve for y.
[tex]14-12=y[/tex][tex]y=2[/tex]Final answer:
The cost of a student ticket = $2.
