The total cost, in dollars, to rent a surfboard consists
of a $25 service fee and a $10 per hour rental fee. A
person rents a surfboard for t hours and intends to
spend a maximum of $75 to rent the surfboard.
Which inequality represents this situation?
A) 10t ≤ 75
B) 10 + 25t ≤ 75
C) 25t ≤ 75
D) 25 + 10t ≤ 75


To represent the situation mathematically, the total cost to rent a surfboard consists of a $25 service fee plus $10 for each hour rented.

Let $ t $ be the number of hours the surfboard is rented. The total cost is therefore:

\[
\text{Total Cost} = 25 + 10t
\]

The person wants to spend a maximum of $75, so we set up the inequality as:

\[
25 + 10t \leq 75
\]

Now, compare this to the answer choices:

- A) $ 10t \leq 75 $ — This does not include the service fee, so it’s incorrect.
- B) $ 10 + 25t \leq 75 $ — This swaps the rates and incorrectly models the situation.
- C) $ 25t \leq 75 $ — This also ignores the $25 service fee and is incorrect.
- D) $ 25 + 10t \leq 75 $ — This matches the inequality we derived.

Therefore, the correct answer is **D**.

Do you need more details or have any questions?

Here are 5 related questions for further practice:
1. If the person rents the surfboard for 4 hours, what will the total cost be?
2. How many hours can a person rent the surfboard if they only want to spend $50?
3. If the service fee increases to $30, what would the new inequality be?
4. What would the inequality look like if the rental fee was $15 per hour instead of $10?
5. If the person has $100 to spend, how many hours can they rent the surfboard?

**Tip:** When solving inequalities, always pay attention to whether you need to reverse the inequality symbol, which happens when multiplying or dividing by a negative number.

The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of $75 to rent the surfboard. Which inequality represents this situation?
A) 10t ≤ 75
B) 10 + 25t ≤ 75
C) 25t ≤ 75
D) 25 + 10t ≤ 75

Learn how to solve the surfboard rental inequality problem where the total cost consists of a $25 service fee and a $10 per hour rental fee. This algebraic problem involves setting up and solving inequalities. Suitable for students in Grades 6-8.

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