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 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.

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 yes, it is a viable option.

Answer 1

To determine the suitable inequality and whether selling 725 bars is a viable option for the adventure club, let’s analyze the situation.

1. Revenue from selling candy bars: The club sells the bars for $2 each. If they sell \( b \) bars, the total revenue is \( 2b \).

2. Profit calculation: The cost of buying the bars is $400. Therefore, the profit from selling the bars can be expressed as: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

3. Setting up the inequality: The club needs to make at least $1,000 in profit. This leads us to the inequality: \[ 2b - 400 \geq 1000 \]

4. Solve the inequality: Now, let’s solve this inequality for \( b \): \[ 2b - 400 \geq 1000 \] \[ 2b \geq 1000 + 400 \] \[ 2b \geq 1400 \] \[ b \geq 700 \]

5. Evaluating the 725 bars option: Since 725 bars are greater than 700, selling 725 bars will allow the club to make a profit that meets their requirement.

6. Conclusion: Therefore, the inequality that represents this problem is: \[ 2b - 400 \geq 1000 \] And since \( b = 725 \) satisfies this inequality, the answer is:

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