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 yes, it is a viable option.

Answer 1

To determine the correct inequality representing this problem, we need to define the variables first:

• Let \( b \) be the number of candy bars sold.
• The revenue from selling \( b \) candy bars is \( 2b \) dollars (since each bar sells for $2).
• The initial cost of purchasing the bars is $400.

To break even and to achieve their goal of making at least $1,000 profit, we can set up the inequality based on the profit formula:

\[ \text{Profit} = \text{Revenue} - \text{Cost} \] \[ \text{Profit} = 2b - 400 \]

To find the minimum profit needed:

\[ 2b - 400 \geq 1000 \]

This gives us the inequality that we are solving:

\[ 2b \geq 1400 \]

Now, we can simplify this to find the minimum number of candy bars they need to sell:

\[ b \geq 700 \]

Next, we check if selling 725 bars is enough:

Calculating the revenue from selling 725 bars:

\[ \text{Revenue} = 2 \times 725 = 1450 \] \[ \text{Profit} = 1450 - 400 = 1050 \]

Since 1050 is greater than 1000, selling 725 bars will indeed cover the cost and meet the profit requirement.

Thus, the correct response is:

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