Math word problem Pre- Algebra

Question

A hockey season ticket holder pays $72.48 for her tickets plus $6 for a program to each game . A second person pays $18.08 for a ticket to every game , but doesn't buy programs. Write an equation that shows when the two fans will pay the same amount . In how many games will they have paid in the same amount?

Answer 1

First, notice that this problem says nothing about how many games these people attend. We can probably assume that, for the same amount of money spent, the season ticket holder can attend more games than the single ticket buyer. We do know how much the season ticket holder paid & can use this as a kind of standard for comparison in this problem.

 

Let's try to put this into an equation using a variable.

 

However many games the season ticket holder attends, she spends an additional $6 for a program book. Let x equal the number of games:

6x+72.48 (this is the total amount spent by the season ticket holder)

 

The other person spends $18.08 per ticket & buys nothing else. Again, let x equal the number of games:

18.08x

 

We want to know when these two people will have spent the same amount:

6x+72.48=18.08x

 

When you solve for x, that solution will be the number of games they can both attend & spend the same amount of money. Manipulate the equation using some basic operations:

 

6x=18.08x-72.48 (subtract 72.48 from each side)

-12.08x=-72.48 (subtract 18.08 from each side)

x=6 (divide each side by -12.08)