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Let's solve the problems on the page one by one.

### Problem 7:
**Given:**
- Ramon rented a sprayer and a generator.
- First job: Used both for 6 hours at a total cost of $90.
- Second job: Used the sprayer for 4 hours and the generator for 8 hours at a total cost of $100.

Let:
- $ x $ be the hourly cost of the sprayer.
- $ y $ be the hourly cost of the generator.

We can set up the following system of equations based on the given information:

\[
6x + 6y = 90 \quad \text{(from the first job)}
\]
\[
4x + 8y = 100 \quad \text{(from the second job)}
\]

We will solve this system of equations.

### Step 1: Simplify the equations
1. From the first equation:
   \[
   6x + 6y = 90 \quad \Rightarrow \quad x + y = 15 \quad \text{(dividing by 6)}
   \]

2. From the second equation:
   \[
   4x + 8y = 100 \quad \Rightarrow \quad 2x + 4y = 50 \quad \text{(dividing by 2)}
   \]

### Step 2: Solve the system
1. From the first simplified equation:
   \[
   x + y = 15
   \]
   \[
   x = 15 - y
   \]

2. Substitute this into the second equation:
   \[
   2(15 - y) + 4y = 50
   \]
   \[
   30 - 2y + 4y = 50
   \]
   \[
   2y = 20
   \]
   \[
   y = 10
   \]

3. Substitute $ y = 10 $ back into $ x + y = 15 $:
   \[
   x + 10 = 15
   \]
   \[
   x = 5
   \]

### Conclusion for Problem 7:
- The hourly cost of the sprayer is $ x = 5 $ dollars.
- The hourly cost of the generator is $ y = 10 $ dollars.

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Here are 5 questions to expand this topic:
1. How do you solve a system of equations using substitution or elimination?
2. What are alternative methods to solve linear systems (e.g., graphing)?
3. How can systems of equations be applied in real-life scenarios like business or engineering?
4. How would this problem change if there were three unknowns instead of two?
5. What happens if two equations in a system are dependent?

**Tip:** Always simplify the equations as much as possible to make solving them easier.

Ramon rented a sprayer and a generator. On his first job, he used each piece of equipment for 6 hours at a total cost of $90. On his second job, he used the sprayer for 4 hours and the generator for 8 hours at a total cost of $100. What was the hourly cost of each piece of equipment?

Learn how to solve a system of equations to find the hourly cost of a sprayer and a generator. Ramon used both for different hours at specific costs. This problem covers algebraic concepts like linear equations and substitution, suitable for students in Grades 8-10.

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