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)

Question

Responses

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.
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.

Answer 1

To determine the correct inequality and viability of selling 725 candy bars, let’s analyze the situation step by step.

1. Define the variables:
   Let \( b \) represent the number of candy bars sold.

2. Selling price and costs:

   • Each candy bar sells for $2, so the total revenue from selling \( b \) bars is \( 2b \).
   • The club bought the bars for $400.

3. Profit calculation:
   Profit is calculated as the total revenue minus the costs: \[ \text{Profit} = 2b - 400 \]

4. Goal:
   The club needs to make at least $1,000 in profit. Thus, we set up the inequality: \[ 2b - 400 \geq 1000 \]

5. Solve the inequality:
   Adding 400 to both sides: \[ 2b \geq 1400 \] Dividing by 2: \[ b \geq 700 \]

6. Substitute \( b = 725 \):
   Now we check if selling 725 bars is a viable option: \[ 2(725) - 400 = 1450 - 400 = 1050 \] Since \( 1050 \geq 1000 \), selling 725 bars will yield a profit greater than the minimum required.

Based on this analysis, the correct inequality is: \[ 2b - 400 \geq 1000 \] And selling 725 candy bars is a viable option.

Therefore, the final response is: 2b−400≥1000, and yes, it is a viable option.