Question

The Stars Basketball League charges $40 entry fee and $10 per game. The Rockets Basketball League charges $100 entry fee and $5 per game. After how many games will the cost of The Stars Basketball League be the same as The Rockets Basketball League?

Answer 1

Given

First, let's summarize the data we have.

Stars Basket league

$40 entry fee and $10 per game

Rockets Basket league

$100 entry fee and $5 per game

After how many games will the cost of The Stars Basketball League be the same as The Rockets Basketball League?

Procedure

Let's write the two previous texts in mathematical expressions to calculate the total cost. We will define the variable x as the number of games attended and the variable y as the total cost after x games.

$\begin{gathered} y=40+10x \\ y=100+5x \end{gathered}$

Now we are going to equal the two equations because we want to know how many are games.

$\begin{gathered} 40+10x=100+5x\text{ } \\ 10x-5x=100-40 \\ 5x=60 \\ x=60/5 \\ x=30 \end{gathered}$

In 30 games the two leagues cost the same.