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 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.
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.

Answer 1

To determine the correct inequality and whether 725 bars are a viable option, let's analyze the situation step-by-step.

1. The club sells each candy bar for $2, so the revenue from selling \( b \) bars is \( 2b \).
2. They bought the bars for $400, so their total cost is $400.
3. They need to make a profit of at least $1,000 to go on their trip. Thus, their profit can be expressed as:
\[
\text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400
\]
4. To find the condition for the profit to be at least $1,000, we set up the inequality:
\[
2b - 400 \geq 1000
\]

Next, let's solve the inequality:

\[
2b - 400 \geq 1000
\]
Add 400 to both sides:
\[
2b \geq 1400
\]
Divide both sides by 2:
\[
b \geq 700
\]

This means that the club needs to sell at least 700 candy bars to make a profit of at least $1,000.

Now, let's evaluate whether the club's purchase of 725 bars is viable:

Since \( 725 \) (the number of bars they have) is greater than \( 700 \) (the minimum needed), they will indeed make enough profit.

To summarize:

- The inequality that represents the problem is \( 2b - 400 \geq 1000 \).
- Selling 725 bars is a viable option because:
\[
2(725) - 400 = 1450 - 400 = 1050 \quad (\text{Profit} = 1050 \geq 1000)
\]

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