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 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.

Answer 1

To solve this problem, we need to set up an inequality based on the information provided.

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

2. The club spent $400 to buy the bars, so their profit would be the revenue minus the cost. This can be expressed as: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

3. The club needs to make at least $1,000 in profit to go on the trip. Therefore, we set up the inequality: \[ 2b - 400 \geq 1000 \]

Now let's solve this inequality:

\[ 2b - 400 \geq 1000 \]

Adding 400 to both sides gives:

\[ 2b \geq 1400 \]

Dividing by 2:

\[ b \geq 700 \]

This means the club needs to sell at least 700 bars to make the desired profit.

Since the club has 725 bars, which is greater than 700, they can sell enough bars to make at least $1,000 in profit.

Therefore, the correct inequality that represents the problem is:

\[ 2b - 400 \geq 1000 \]

And since 725 bars can be sold to achieve the goal, the answer is:

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