Question

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 less 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 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 yes, it is a viable option.

Answer 1

To determine the correct inequality and viability of selling 725 candy bars, let’s analyze the situation step by step.

1. **Define the variables:**
Let \( b \) represent the number of candy bars sold.

2. **Selling price and costs:**
- Each candy bar sells for $2, so the total revenue from selling \( b \) bars is \( 2b \).
- The club bought the bars for $400.

3. **Profit calculation:**
Profit is calculated as the total revenue minus the costs:
\[
\text{Profit} = 2b - 400
\]

4. **Goal:**
The club needs to make at least $1,000 in profit. Thus, we set up the inequality:
\[
2b - 400 \geq 1000
\]

5. **Solve the inequality:**
Adding 400 to both sides:
\[
2b \geq 1400
\]
Dividing by 2:
\[
b \geq 700
\]

6. **Substitute \( b = 725 \):**
Now we check if selling 725 bars is a viable option:
\[
2(725) - 400 = 1450 - 400 = 1050
\]
Since \( 1050 \geq 1000 \), selling 725 bars will yield a profit greater than the minimum required.

Based on this analysis, the correct inequality is:
\[
2b - 400 \geq 1000
\]
And selling 725 candy bars **is** a viable option.

Therefore, the final response is:
**2b−400≥1000, and yes, it is a viable option.**