Question

The Mitchell family is renting a boat for the day. The boat rental has a flat fee of $100 plus $20 for each hour. They
have to pay for a whole hour even if they are not out on the lake for a whole hour. For example, if they rent the boat
for 3 and one-half hours, they have to pay for 4 hours. If they want to spend $250 or less on the boat rental for the
day, how many hours can they rent the boat? Formulate an inequality and solve.
a) 100 + 20x ≤ 250; They can boat for 7 hours.
b) 100 + 20x ≥ 250; They can boat for 8 hours.
c) 100 + 20x ≤ 250; They can boat for 8 hours.
d)100 + 20x ≥ 250; They can boat for 7

Answer 1

To formulate the inequality based on the problem statement, we can set the following variables:

- Let \( x \) be the number of hours they rent the boat.

The total cost of the boat rental can be expressed as:

\[
\text{Total Cost} = 100 + 20x
\]

According to the problem, they want to spend $250 or less on the rental. So, we can express this as an inequality:

\[
100 + 20x \leq 250
\]

Now, let's solve the inequality:

1. Subtract 100 from both sides:

\[
20x \leq 250 - 100
\]

2. Simplify the right side:

\[
20x \leq 150
\]

3. Divide both sides by 20:

\[
x \leq \frac{150}{20}
\]

4. Simplify the fraction:

\[
x \leq 7.5
\]

Since they have to pay for a whole hour, we need to round down to the greatest whole number less than or equal to 7.5. Therefore, they can rent the boat for a maximum of 7 hours.

So the correct option is:

**a) 100 + 20x ≤ 250; They can boat for 7 hours.**