Question

The school that Stefan goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 1 senior citizen ticket and 14 student tickets for a total of $225. The school took in $120 on the second day by selling 7 senior citizen tickets and 1 student ticket. What is the price each of one senior citizen ticket and one student ticket?

Answer 1

x = price of a senior ticket

y = price of a student ticket

First day: x + 14y = $225

Second day: 7x + y = $120

Let's solve this system of equations by substitution

Subtract 14y from both sides on our first equation

First day: x = $225 - 14y

Substitute this value into our second equation for x

7($225 - 14y) + y = $120

Distribute the 7

$1575 - 98y + y = $120

Combine like terms

$1575 - 97y = $120

Subtract $1575 from both sides

-97y = -1455

Divide both sides by -97

y = $15

Plug this value into our first equation

x + 14(15) = $225

Simplify

x + $210 = $225

Subtract $210 from both sides

x = $15

The senior and student tickets cost $15