The "Bouncy" Company offers two types of bouncy houses to jump on. It cost $75 for the small one and $125 for the large one per day. The company's goal is to make at least $1175 per day so far today they have rented out 6 large bouncy houses and 3 small. Select all possible solutions for the number of small houses they still need to rent to make at least $1175

We can solve this problem by setting up an inequality that represents the total revenue needed.

### Step 1: Calculate the current revenue
- The company has rented 6 large bouncy houses at $125 each, so:
  \[
  \text{Revenue from large houses} = 6 \times 125 = 750
  \]
- The company has rented 3 small bouncy houses at $75 each, so:
  \[
  \text{Revenue from small houses} = 3 \times 75 = 225
  \]
- The total revenue so far is:
  \[
  \text{Total revenue so far} = 750 + 225 = 975
  \]

### Step 2: Set up the inequality
- The company's goal is to make at least $1175, so the remaining revenue needed is:
  \[
  \text{Remaining revenue needed} = 1175 - 975 = 200
  \]
- Let $ x $ be the number of small houses they still need to rent. Since each small house costs $75, the revenue from renting $ x $ additional small houses is $ 75x $. This gives us the inequality:
  \[
  75x \geq 200
  \]

### Step 3: Solve the inequality
\[
x \geq \frac{200}{75} \approx 2.67
\]
Since $ x $ must be a whole number, $ x \geq 3 $.

### Step 4: Conclusion
The company needs to rent at least **3 more small bouncy houses** to meet their goal of at least $1175.

### Would you like any further clarification or details?

---

### Additional questions to consider:
1. What if the company wanted to make at least $1500 per day? How would the equation change?
2. How much revenue would be generated if they rented 4 more small houses?
3. What would happen if the price of a large bouncy house increased to $150? How would that affect the solution?
4. What is the maximum number of small houses they would need to rent if the large ones were unavailable?
5. How would the inequality change if both types of houses were offered at a discounted rate?

### Tip:
When solving inequalities involving money or quantities, always check whether your solution needs to be rounded to the nearest whole number, as fractional answers may not be practical in real-life scenarios.

The 'Bouncy' Company offers two types of bouncy houses to jump on. It cost $75 for the small one and $125 for the large one per day. The company's goal is to make at least $1175 per day so far today they have rented out 6 large bouncy houses and 3 small. Select all possible solutions for the number of small houses they still need to rent to make at least $1175.

Learn how to solve a real-life inequality problem involving bouncy house rentals. This algebraic problem teaches how to calculate revenue, set up inequalities, and solve for the number of small houses needed to meet a minimum daily revenue of $1175. Suitable for students in Grades 6-8.

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