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 greater 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 less 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 whether selling 725 bars is viable for making at least $1000 profit, let's break down the problem.

1. Define the variables:

   • Let \( b \) be the number of candy bars sold.

2. Determine the total revenue from selling the bars:

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

3. Calculate the profit:

   • The cost to buy the bars is $400. Therefore, the profit is given by the total revenue minus the cost: \[ \text{Profit} = 2b - 400. \]

4. Set up the inequality for profit:

   • The club needs to make at least $1000: \[ 2b - 400 \geq 1000. \]

5. Solve the inequality to find the required number of bars: \[ 2b - 400 \geq 1000 \] \[ 2b \geq 1400 \] \[ b \geq 700. \]

This means the club needs to sell at least 700 bars to make a profit of at least $1000.

6. Evaluate the feasible option of selling 725 bars:
   • The club plans to sell 725 bars, and since 725 is greater than 700, selling these bars will indeed cover the needed amount for the trip.

So the correct response to represent the problem is: \( 2b - 400 \geq 1000 \), and yes, it is a viable option.