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?(1 point)

Question

Responses

2b−400≤1000 , and yes, it is a viable option.
2 b minus 400 less than or equal to 1000 , and yes, it is a viable option.

2b−400≤1000 , and no, it is not a viable option.
2 b minus 400 less than or equal to 1000 , and no, it is not a viable option.

2b−400≥1000 , and yes, it is a viable option.
2 b minus 400 greater than or equal to 1000 , and yes, it is a viable option.

2b−400≥1000 , and no, it is not a viable option.

Answer 1

To determine the correct inequality and whether selling 725 candy bars is a viable option, let’s analyze the problem step by step:

1. Revenue from selling bars: The candy bars sell for $2 each, so if \( b \) represents the number of bars sold, the revenue from selling the bars is \( 2b \).

2. Cost of the bars: The club bought the 725 bars for $400. Thus, the cost is $400.

3. Profit calculation: The profit \( P \) can be calculated as the revenue minus the cost: \[ P = \text{Revenue} - \text{Cost} = 2b - 400 \]

4. Minimum profit requirement: The club needs to make at least $1,000, so we set up the inequality: \[ 2b - 400 \geq 1000 \]

5. Solving the inequality:

   • Add 400 to both sides: \[ 2b \geq 1400 \]
   • Divide both sides by 2: \[ b \geq 700 \]

6. Evaluating the option of selling 725 bars: Since 725 bars is greater than 700, selling 725 bars does meet the club's requirement for making at least $1,000 in profit.

Based on this analysis, the correct inequality is: \[ 2b - 400 \geq 1000 \] and since selling 725 bars is sufficient to meet the profit requirement, the answer is: 2b - 400 ≥ 1000, and yes, it is a viable option.