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 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 less than or equal to 1000 , and yes, it is a viable option.

2b−400≤1000 , and no, it is not a viable option.

Answer 1

To solve this problem, let's define the variables and set up the inequality:

• Let \( b \) be the number of candy bars sold.
• Each candy bar sells for $2, so selling \( b \) bars brings in \( 2b \) dollars.
• The club spent $400 on the candy bars.
• The club needs to make at least $1,000 in profit.

The profit can be calculated as: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

We need this profit to be at least $1,000: \[ 2b - 400 \geq 1000 \]

Now let's solve this inequality for \( b \):

1. Add 400 to both sides: \[ 2b \geq 1400 \]
2. Divide by 2: \[ b \geq 700 \]

This means that the club needs to sell at least 700 candy bars to achieve their goal of making $1,000 in profit.

Now, let's check if selling the 725 bars is a viable option. Since 725 is greater than 700, selling 725 bars would indeed allow them to meet their goal.

Now, looking at the options provided:

The correct inequality is: \[ 2b - 400 \geq 1000 \]

And since 725 bars is sufficient to meet the requirement, the answer would be: 2b−400≥1000, and yes, it is a viable option.