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?(1 point) 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 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.

Answer 1

To analyze the problem, let's break it down step by step:

1. The club sells candy bars for $2 each. If they sell \( b \) bars, their income will be \( 2b \).

2. The club's cost to purchase the bars is $400.

3. To find out how much profit they need to make at least $1,000, we can formulate the following inequality based on their profit: \[ \text{Profit} = \text{Income} - \text{Cost} \] \[ \text{Profit} = 2b - 400 \] To meet their goal of at least $1,000 profit, we set up the inequality: \[ 2b - 400 \geq 1000 \]

4. Next, we can solve this inequality: \[ 2b - 400 \geq 1000 \] Adding 400 to both sides: \[ 2b \geq 1400 \] Dividing both sides by 2: \[ b \geq 700 \]

5. Given that the club has 725 bars, we can see that: \[ 725 \geq 700 \] Which confirms that selling 725 bars meets the requirement.

Therefore, the inequality that best represents the problem is: \[ 2b - 400 \geq 1000 \]

And since the club has 725 bars, which satisfies \( b \geq 700 \), it is indeed a viable option.

So the correct response is: 2b−400≥1000 , and yes, it is a viable option.