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 greater 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.
2 b minus 400 less than or equal to 1000 , and no, it is not a viable option.
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Answer 1

To determine the inequality that best represents the problem, let's break it down:

1. The club sells candy bars for $2 each, so if they sell \( b \) bars, their revenue can be represented as \( 2b \).
2. The club's total cost for the bars is $400.
3. To check if they can make at least $1,000, we set up the equation for profit, which is represented as: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]
4. The requirement is that the profit should be at least $1,000, so we can set up the inequality: \[ 2b - 400 \geq 1000 \]

Now, we can rearrange the inequality to see if the option to sell 725 bars is viable:

\[ 2b - 400 \geq 1000 \ 2b \geq 1000 + 400 \ 2b \geq 1400 \ b \geq 700 \]

Since the club has 725 bars, we plug this into \( b \):

\[ 725 \geq 700 \]

This inequality is true, which means that selling 725 bars is indeed a viable option.

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