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 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.

Answer 1

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

1. The cost of the candy bars: The club bought 725 bars for $400.
2. Each candy bar sells for $2; therefore, if they sell \( b \) bars, the revenue from selling them is \( 2b \).
3. The club needs to make at least $1,000 profit to go on the trip.

The profit can be defined as:

\[
\text{Profit} = \text{Revenue} - \text{Cost}
\]

Which translates to:

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

To ensure they make at least $1,000, we set up the inequality:

\[
2b - 400 \geq 1000
\]

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

\[
2b \geq 1000 + 400
\]
\[
2b \geq 1400
\]
\[
b \geq 700
\]

Now, since they have 725 bars:
- If \( b = 725 \), then the profit calculation is:
\[
\text{Profit} = 2(725) - 400 = 1450 - 400 = 1050
\]

This profit, $1050, is indeed more than $1,000.

Thus, the inequality that best represents the problem is:

\[
2b - 400 \geq 1000
\]

And since 725 bars will yield the required profit, the correct answer is:

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