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

A 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.

B 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.

C 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.

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

1 answer

To find the correct inequality and determine whether selling 725 Candy bars is a viable option, we first need to set up the problem.

Step 1: Establish the sales and profit.

The candy bars are sold for $2 each. If the club sells \( b \) bars, their revenue \( R \) from selling the bars is:

\[ R = 2b \]

Step 2: Calculate the profit.

The cost of the candy bars that the club bought is $400. Therefore, the profit \( P \) from selling \( b \) bars is:

\[ P = R - \text{Cost} = 2b - 400 \]

The club needs to make at least $1,000 in profit, which means we can set up the following inequality:

\[ 2b - 400 \geq 1000 \]

Step 3: Solve the inequality.

To find the minimum number of bars they need to sell to make at least $1,000 profit, we can solve the inequality:

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

Step 4: Check if selling 725 bars is viable.

Now, check if selling 725 bars meets the profit requirement:

\[ P = 2(725) - 400 \] \[ P = 1450 - 400 \] \[ P = 1050 \]

Since \( 1050 \geq 1000 \), selling 725 bars will indeed allow the club to reach their profit goal.

Conclusion:

The inequality representing the problem is:

\[ 2b - 400 \geq 1000 \]

And since selling 725 bars yields a profit greater than $1,000, the correct answer is:

D: 2b - 400 ≥ 1000, and yes, it is a viable option.