Use the information given to answer the question.

A family rents a personal watercraft and a speedboat for use on a lake.

To rent the personal watercraft, the family pays an 
 security deposit in addition to a rental fee of 
 per hour.
To rent the speedboat, the family pays a 
 security deposit in addition to a rental fee of 
 per hour.
Part A

If the total cost for the family to rent the personal watercraft and speedboat for the same number of hours is 
, which equation could be used to determine the number of hours, 
, the family rents both the personal watercraft and the speedboat?

Responses

Let's break this down with the information provided:

1. **Personal Watercraft:**
   - Security deposit = \( D_1 \) (a fixed cost).
   - Rental fee = \( R_1 \) per hour.

2. **Speedboat:**
   - Security deposit = \( D_2 \) (a fixed cost).
   - Rental fee = \( R_2 \) per hour.

3. **Total cost:** The total amount the family spends to rent both the personal watercraft and the speedboat for \( h \) hours is \( C \).

The **total cost** includes the sum of both security deposits and the hourly rental fees. Since the family rents both the personal watercraft and the speedboat for the same number of hours, the total cost can be expressed as:

\[
C = D_1 + D_2 + h \cdot (R_1 + R_2)
\]

This equation accounts for:
- The fixed cost of both security deposits \( (D_1 + D_2) \).
- The cost of renting both the personal watercraft and the speedboat for \( h \) hours at their respective hourly rates \( R_1 \) and \( R_2 \).

Thus, the equation to determine the number of hours \( h \) the family rents both items is:

\[
C = D_1 + D_2 + h(R_1 + R_2)
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the equation change if the number of hours for renting the watercraft and speedboat were different?
2. What if there were additional costs per hour, such as fuel or maintenance fees?
3. How can you solve this equation if the total cost \( C \) and other values are known?
4. How would a discount on the security deposits affect the total cost equation?
5. How does the equation change if the rental is over multiple days?

**Tip:** Always double-check that all fixed and variable costs are included in the total cost equation to avoid missing important terms.

If the total cost for the family to rent the personal watercraft and speedboat for the same number of hours is C, which equation could be used to determine the number of hours, h, the family rents both the personal watercraft and the speedboat?

Learn how to determine the number of hours a family rents both a personal watercraft and a speedboat using a linear equation. This example covers algebraic concepts including cost analysis and linear equations, suitable for students in Grades 6-8.

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