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 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 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.
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.

Answer 1

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

1. **Selling Price per Bar:** $2
2. **Number of Bars:** 725
3. **Cost of Bars:** $400
4. **Profit Goal:** At least $1,000

The total revenue from selling \( b \) bars at $2 each is represented by \( 2b \). The club’s profit is calculated by subtracting the cost from the revenue:

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

To meet the profit goal, this value must be at least $1,000:

\[
2b - 400 \geq 1000
\]

This is the inequality that we need.

Now, let's determine if selling 725 bars is a viable option:

Substituting \( b = 725 \) into the inequality:

\[
2(725) - 400 \geq 1000
\]

Calculating the left-hand side:

\[
1450 - 400 = 1050
\]

Now we check if this is greater than or equal to 1000:

\[
1050 \geq 1000 \quad \text{(which is true)}
\]

Since the inequality holds true, we conclude that selling 725 bars is indeed a viable option.

**Final answer:**
- The correct inequality is \( 2b - 400 \geq 1000 \), and yes, it is a viable option.