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.

1 answer

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.