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.