Amanda rented a bike from Ted's Bikes.
It costs $13 for the helmet plus $3.75 per hour.
If Amanda paid about $33.63, how many hours did she rent the bike?

a) Let  = the number of hours she rented the bike. Write the equation you would use to solve this problem.

b) Now solve your equation

Amanda rented the bike for  hours. (Round your answer to the nearest tenth of an hour.)

Let's break down the problem step by step.

### Part (a): Write the Equation

Let $ h $ represent the number of hours Amanda rented the bike. 

The total cost Amanda paid is the sum of the cost of the helmet and the cost of renting the bike for $ h $ hours. The cost for renting the bike is given by $3.75 per hour. Therefore, the equation to solve is:

\[
13 + 3.75h = 33.63
\]

### Part (b): Solve the Equation

Now, we'll solve the equation for $ h $.

1. **Subtract 13 from both sides:**

\[
3.75h = 33.63 - 13
\]

\[
3.75h = 20.63
\]

2. **Divide both sides by 3.75 to solve for $ h $:**

\[
h = \frac{20.63}{3.75}
\]

\[
h \approx 5.5 \text{ hours}
\]

So, Amanda rented the bike for approximately **5.5 hours**.

Would you like any more details or have any questions about this solution?

### Follow-Up Questions:
1. How would the equation change if the helmet cost was $15 instead of $13?
2. What would be the total cost if Amanda rented the bike for 7 hours?
3. If Amanda had a discount coupon that reduced the helmet price by $3, how would that affect the equation and solution?
4. How many hours could Amanda rent the bike if she had a budget of $25?
5. If the hourly rate increased to $4, how would that change the number of hours Amanda could rent the bike for $33.63?

### Tip:
When solving equations, always isolate the variable on one side to find its value.

Learn how to calculate the number of hours Amanda rented a bike based on the total cost paid, including the cost of the helmet and the per-hour rental rate. Step-by-step solution provided.

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