Question

The adventure club is selling candy bars to go on their annual outing. The bars sell for $2 a bar. The club bought 725 bars for $400. The club needs to make at least $1,000 to go on their trip. Which inequality best represents this problem, and are the 725 bars a viable option to make enough profit?

Answer 1

To determine the appropriate inequality and whether the club can make enough profit, let's break this down step by step.

1. **Cost and Selling Price:**
- The club bought 725 bars at a total cost of $400.
- Each candy bar sells for $2.

2. **Determine Revenue:**
- If they sell all 725 bars, the total revenue generated from selling the bars would be:
\[
\text{Revenue} = \text{Number of Bars} \times \text{Selling Price per Bar} = 725 \times 2 = 1450
\]

3. **Profit Calculation:**
- Profit is defined as the revenue minus costs:
\[
\text{Profit} = \text{Revenue} - \text{Cost} = 1450 - 400 = 1050
\]

4. **Required Profit:**
- The club needs to make at least $1,000 to afford their trip.

5. **Set up the Inequality:**
- We need to check if their profit meets or exceeds the required amount:
\[
\text{Profit} \geq 1000
\]
- Substituting the profit formula gives:
\[
1450 - 400 \geq 1000
\]
- Which simplifies to:
\[
1050 \geq 1000
\]

6. **Conclusion:**
Since $1050$ is greater than $1000$, the inequality \( \text{Profit} \geq 1000 \) is satisfied.

Therefore, the inequality that represents the situation is:
\[
\text{Revenue} - \text{Cost} \geq 1000
\]
or explicitly,
\[
725 \cdot 2 - 400 \geq 1000
\]
The calculation shows that selling 725 bars is indeed a viable option for the club, as they would make a profit of $1050, which exceeds their requirement of at least $1000.