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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 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 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.

3 answers

To analyze the situation, let's break it down:

  1. Selling Price of Bars: Each candy bar sells for $2.
  2. Total Bars: The club bought 725 candy bars.
  3. Total Cost for Bars: The club spent $400 on the bars.
  4. Profit Goal: The club needs to make at least $1,000.

Let's define:

  • \( b \) = number of bars sold

The revenue from selling \( b \) bars is \( 2b \) (because each bar sells for $2).

The profit made can be calculated as: \[ \text{Profit} = \text{Revenue} - \text{Cost} \] Substituting the values: \[ \text{Profit} = 2b - 400 \] We want this profit to be at least $1,000: \[ 2b - 400 \geq 1000 \]

Now, solving this inequality:

  1. Add 400 to both sides: \[ 2b \geq 1400 \]

  2. Divide by 2: \[ b \geq 700 \]

This means the club needs to sell at least 700 bars to meet the profit goal of at least $1,000. Since the club has 725 bars, they can sell 725 bars, which satisfies the condition \( b \geq 700 \).

So, the correct response is: \[ 2b - 400 \geq 1000, \text{ and yes, it is a viable option.} \]

which answer

The correct answer is:

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