1. Susan is renting a limo for prom. There is a one-time charge of [tex]$100[/tex], plus an hourly rate of [tex]$45[/tex]. Her total cost for the night was [tex]$370[/tex]. How many hours did Susan rent the limo for?

- Let Statement: Let $ x $ represent the number of hours Susan rented the limo.
- Equation: $ 100 + 45x = 370 $
- Solve the Equation:

\[
45x = 370 - 100 \\
45x = 270 \\
x = \frac{270}{45} \\
x = 6
\]

- Answer: Susan rented the limo for 6 hours.

2. Ethan charged his customers a flat fee of [tex]$25[/tex] to fix computers. Then he charged [tex]$20[/tex] for each hour that he was fixing the computer. If Ethan made [tex]$175[/tex] for his first customer of the day, how many hours did he spend working on the computer?

- Let Statement: Let $ y $ represent the number of hours Ethan worked on the computer.
- Equation: $ 25 + 20y = 175 $
- Solve the Equation:

\[
20y = 175 - 25 \\
20y = 150 \\
y = \frac{150}{20} \\
y = 7.5
\]

- Answer: Ethan spent 7.5 hours working on the computer.

Sure, let's solve each problem step-by-step:

Problem 1: Susan renting a limo

1. Let statement:
- Let [tex]$ h $[/tex] be the number of hours Susan rented the limo.

2. Write an equation:
- The total cost consists of a one-time charge and an hourly rate. So, the equation is:
[tex]\[
100 + 45h = 370
\][/tex]
- Here, 100 is the one-time charge, 45 is the hourly rate, and 370 is the total cost.

3. Solve the equation:
- Subtract 100 from both sides:
[tex]\[
45h = 270
\][/tex]
- Divide by 45 to isolate [tex]$ h $[/tex]:
[tex]\[
h = 6
\][/tex]

4. State your answer:
- Susan rented the limo for 6 hours.

---

Problem 2: Ethan fixing a computer

1. Let statement:
- Let [tex]$ t $[/tex] be the number of hours Ethan worked on the computer.

2. Write an equation:
- The total earnings consist of a flat fee and an hourly charge. So, the equation is:
[tex]\[
25 + 20t = 175
\][/tex]
- Here, 25 is the flat fee, 20 is the hourly charge, and 175 is the total earnings.

3. Solve the equation:
- Subtract 25 from both sides:
[tex]\[
20t = 150
\][/tex]
- Divide by 20 to isolate [tex]$ t $[/tex]:
[tex]\[
t = 7.5
\][/tex]

4. State your answer:
- Ethan worked on the computer for 7.5 hours.