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.