Question

A group of 10 students went to a football game at their university. They each bought a ticket for $x and spent $20 on a t-shirt. A group of 4 adulis went to the same football game and paid five times as much for each of their tickets as each student. The group of adults also bought a long- sleeved t-shirt for $25 each. The group of students spent the same amount as the group of adults. What is the cost of each student ticket? Write and solve an equation to model the problem. Explain the meaning of the solution.

Answer 1

From the statement of the equation we can express the money spent by each student (s) with this equation:

s=x+20

where x is the cost of the ticket and 20 is the cost of the t-shirt.

Since we know that there are 10 students in total, we can get the total money spent by the students (ts) by multiplying the equation s=x+20 by 10, like this:

ts=(x+20)*10=10x+200

We know that each ticket cost 5 times more for an adult than for a student, then we can express the equation that models the money spent by each adult (a) like this:

a=5x+25

Where 5x is the cost of the ticket and 25 is the cost of the shirt.

Since there are 4 adults, by multiplying this equation by 4, we can get the total money spent by the group of adults (ta), like this:

ta=(5x+25)*4=20x+100

We are told that the group of students spent the same that the group of adults in total, then we can make the expressions that model the money spent for each group equal like this:

ts=ta

ts=10x+200

ta=20x+100, then:

10x+200=20x+100

By solving for x from this equation we get:

10x+200=20x+100

10x-10x+200-100=20x-10x+100-100

0+100=10x+0

100=10x

10x=100

10x/10=100/10

x=10

Then, the cost of each student ticket is $10