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The problem in the image reads:

**One month Hans rented 9 movies and 7 video games for a total of $74. The next month, he rented 3 movies and 5 video games for a total of $40. Find the rental cost for each movie and each video game.**

This scenario can be represented using a system of two linear equations:

Let:
- $ x $ = rental cost for each movie,
- $ y $ = rental cost for each video game.

From the given information:
1. $ 9x + 7y = 74 $ (First month)
2. $ 3x + 5y = 40 $ (Second month)

Now, let's solve this system of equations to find the values of $ x $ and $ y $.

### Solving the System:

First, we'll use the method of elimination or substitution to solve this system. Let's use elimination:

Multiply the second equation by 3 to align the coefficients of $ x $:

- $ 9x + 7y = 74 $
- $ 9x + 15y = 120 $

Now, subtract the first equation from the second:

\[
(9x + 15y) - (9x + 7y) = 120 - 74
\]
\[
9x + 15y - 9x - 7y = 46
\]
\[
8y = 46
\]
\[
y = \frac{46}{8} = 5.75
\]

Now that we have $ y = 5.75 $ (the rental cost of each video game), substitute this value into one of the original equations to solve for $ x $. We'll use the second equation:

\[
3x + 5(5.75) = 40
\]
\[
3x + 28.75 = 40
\]
\[
3x = 40 - 28.75
\]
\[
3x = 11.25
\]
\[
x = \frac{11.25}{3} = 3.75
\]

### Solution:
- The rental cost for each movie $ x = 3.75 $ dollars.
- The rental cost for each video game $ y = 5.75 $ dollars.

Would you like more details, or do you have any other questions?

Here are 5 related questions:
1. How can systems of equations be solved using substitution instead of elimination?
2. What other real-world situations can be modeled using systems of equations?
3. How would the solution change if one month's total was different?
4. Can this system be solved using a graphical method, and how would that work?
5. How can we verify if our solution is correct by substitution?

**Tip:** When solving systems of equations, it’s important to check your solution by substituting the values back into the original equations.

One month Hans rented 9 movies and 7 video games for a total of $74. The next month he rented 3 movies and 5 video games for a total of $40. Find the rental cost for each movie and each video game.

Learn how to solve a system of equations to find the rental costs of movies and video games. This problem uses algebraic techniques such as the method of elimination and linear systems theory, suitable for Grades 8-10.

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