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 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 set up the inequality for the adventure club's candy bar sales, let's first define the variables and the situation:

• Let \( b \) be the number of candy bars sold.
• The club sells each candy bar for $2, so the total revenue from selling \( b \) bars is \( 2b \).
• The club purchased the bars for $400, so the profit can be calculated as total revenue minus the cost, which is \( 2b - 400 \).
• The club needs to make at least $1,000 to go on their trip, so we want the profit to be greater than or equal to $1,000.

Therefore, we can set up the inequality:

\[ 2b - 400 \geq 1000 \]

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

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

2. Divide both sides by 2: \[ b \geq 700 \]

This means the club must sell at least 700 candy bars to make at least $1,000.

Now, we have to check if selling all 725 bars is a viable option:

• Since \( 725 \) is greater than \( 700 \), selling 725 bars will indeed meet the requirement to make enough profit.

Now let's look at the options given:

• The correct inequality is \( 2b - 400 \geq 1000 \).
• Since 725 bars can be sold to meet the profit requirement, it is a viable option.

The correct answer is: 2b - 400 ≥ 1000, and yes, it is a viable option.