To determine the correct inequality and whether selling 725 bars is a viable option for making at least $1,000 in profit, we need to break down the information provided.
- Selling Price: The candy bars sell for $2 each.
- Cost: The club bought 725 bars for $400.
- Desired Profit: The club wants to make at least $1,000.
Total Revenue from Selling Bars: If \( b \) is the number of bars sold, the revenue from selling \( b \) bars is: \[ R = 2b \]
Profit Calculation: The profit \( P \) can be calculated as: \[ P = R - \text{Cost} \] Substituting \( R \) from above: \[ P = 2b - 400 \]
The club wants to make at least $1,000 in profit, which gives us the inequality: \[ 2b - 400 \geq 1000 \]
Simplifying the Inequality: To find out how many bars need to be sold to meet the profit requirement, we can solve the inequality: \[ 2b - 400 \geq 1000 \] Add 400 to both sides: \[ 2b \geq 1400 \] Divide by 2: \[ b \geq 700 \]
Now, since the club has 725 bars, they can sell up to 725 bars.
Checking Viability: Now we need to check if selling 725 bars meets the requirement we calculated:
- When \( b = 725 \): \[ P = 2(725) - 400 = 1450 - 400 = 1050 \] This profit of $1050 is indeed greater than the required $1,000.
Conclusion
The correct inequality is: \[ 2b - 400 \geq 1000 \] And since the club has 725 bars, yes, it is a viable option.
The correct response is: 2b−400≥1000 , and yes, it is a viable option.
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