A group of friends decides to share a limo for prom. The rental cost is $750 plus $25 fee for each occupant. There is a minimum of 2 passengers, and the limo can hold 14 people write an inequality and solve an inequality to determine how many people can share the limo for less than $120 per person

Let's define the variables first:

- Let $ x $ be the number of people sharing the limo.
- The total cost for the limo rental is $750 plus $25 per occupant.
- Each person wants to spend less than $120.

### Step 1: Write an expression for the total cost per person.
The total cost of the limo for $ x $ occupants is:
\[
750 + 25x
\]

The cost per person is:
\[
\frac{750 + 25x}{x}
\]

### Step 2: Write the inequality.
We want this cost per person to be less than $120, so we write the inequality:
\[
\frac{750 + 25x}{x} < 120
\]

### Step 3: Solve the inequality.

First, multiply both sides of the inequality by $ x $ (assuming $ x > 0 $) to eliminate the denominator:
\[
750 + 25x < 120x
\]

Now, subtract $ 25x $ from both sides:
\[
750 < 95x
\]

Finally, divide both sides by 95:
\[
x > \frac{750}{95}
\]

\[
x > 7.89
\]

Since $ x $ must be a whole number of people, we round up to the next whole number:
\[
x \geq 8
\]

### Step 4: Consider the constraints.
- The limo can hold at most 14 people.
- There is a minimum of 2 passengers.

Thus, the number of people sharing the limo must satisfy:
\[
8 \leq x \leq 14
\]

### Conclusion:
The number of people who can share the limo for less than $120 per person is between 8 and 14.

Would you like to see the details behind the inequality solution, or do you have any questions?

#### Related Questions:
1. What would happen if the maximum capacity of the limo increased to 16 people?
2. How would the result change if the rental cost increased to $900?
3. If the rental fee per occupant increased from $25 to $30, what would the new inequality be?
4. What if each person wanted to spend less than $100 instead of $120?
5. How would the solution change if the minimum number of passengers increased to 4?

**Tip:** When solving inequalities, always consider the impact of constraints, such as minimum and maximum limits.

A group of friends decides to share a limo for prom. The rental cost is $750 plus $25 fee for each occupant. There is a minimum of 2 passengers, and the limo can hold 14 people. Write an inequality and solve an inequality to determine how many people can share the limo for less than $120 per person.

Discover how to solve an inequality to determine how many people can share a limo for less than $120 per person. This algebraic problem involves inequality solving and linear equations, making it perfect for students in Grades 9-12.

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