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 greater 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 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 greater than or equal to 1000 , and no, it is not a viable option.

Answer 1

To determine the correct inequality and the viability of selling 725 candy bars, let's analyze the problem step-by-step:

1. Selling Price per Candy Bar: Each candy bar sells for $2. Therefore, if the club sells \( b \) bars, the revenue from selling these bars will be: \[ \text{Revenue} = 2b \]

2. Cost of Candy Bars: The cost of purchasing the 725 bars was $400.

3. Profit Calculation: The profit is calculated as revenue minus cost: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

4. Profit Requirement: The club needs to make at least $1,000 in profit to go on their trip, which gives the inequality: \[ 2b - 400 \geq 1000 \]

5. Solving the Inequality: \[ 2b - 400 \geq 1000 \] Add 400 to both sides: \[ 2b \geq 1400 \] Divide both sides by 2: \[ b \geq 700 \]

This means the club needs to sell at least 700 candy bars to meet their profit requirement.

6. Evaluating the Viability with 725 Bars: Since the club has 725 bars, and they need to sell at least 700 bars, selling 725 bars is indeed viable.

Thus, the correct response is:

2b−400≥1000 , and yes, it is a viable option.