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Let's solve this problem using a system of linear equations.

Let:
- $ x $ = the cost of a new video game
- $ y $ = the cost of a used video game

The information given translates into two equations based on the purchases:

1. **Friend 1's purchase:** $ 2x + 3y = 104.17 $
2. **Friend 2's purchase:** $ 1x + 6y = 110.09 $

We need to find the values of $ x $ and $ y $. Let’s solve these equations step by step.

### Step 1: Solve for $ x $ using equation 2
From the second equation:
\[
x + 6y = 110.09
\]
\[
x = 110.09 - 6y
\]

### Step 2: Substitute $ x $ in equation 1
Substitute $ x = 110.09 - 6y $ into the first equation:
\[
2(110.09 - 6y) + 3y = 104.17
\]
\[
220.18 - 12y + 3y = 104.17
\]
\[
220.18 - 9y = 104.17
\]
\[
-9y = 104.17 - 220.18
\]
\[
-9y = -116.01
\]
\[
y = \frac{-116.01}{-9}
\]
\[
y = 12.89
\]

So, the cost of a used video game is **$12.89**.

Would you like further details or have any questions?

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Here are 5 related questions for further practice:
1. How much does a new video game cost in this scenario?
2. If Friend 3 buys 3 new and 2 used video games, how much would they pay?
3. What would the cost be if Friend 2 only bought 2 used video games?
4. How would the equations change if the prices were in a different currency?
5. If the cost of a used game increases by 10%, what would the new total be for Friend 1?

**Tip:** When dealing with word problems, always define variables clearly before setting up equations.

Two friends buy new and used video games from a video game store. Friend 1 buys 2 new video games and 3 used video games for a total of $104.17. Friend 2 buys 1 new video game and 6 used video games for a total of $110.09. What is the cost of a used video game, in dollars and cents?

Learn how to solve a system of linear equations to determine the cost of a used video game. This problem involves two friends' video game purchases and uses algebraic methods, such as substitution. Suitable for students in Grades 8-10.

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