The adventure club is selling candy bars to go on their annual outing. The bars sell for $\$ 2$ a bar.

Question

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?

$2b-400\geqslant 1000$ , and yes, it is a viable option.
$2b-400\leqslant 1000$ , and no, it is not a viable option.
$2b-400\leqslant 1000$ , and yes, it is a viable option.
$2b-400\geqslant 1000$ , and no, it is not a viable option

Answer 1

To represent this problem, we can start by defining the variables. Let \( b \) be the number of candy bars sold.

The revenue from selling \( b \) candy bars at \( $2 \) per bar is given by: \[ 2b \]

The cost of purchasing the 725 candy bars is $400. The profit, therefore, is calculated as: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

The club needs to make at least $1000 in profit, which gives us the inequality: \[ 2b - 400 \geq 1000 \]

Now, we can solve this inequality for \( b \): \[ 2b - 400 \geq 1000 \] Add 400 to both sides: \[ 2b \geq 1400 \] Divide both sides by 2: \[ b \geq 700 \]

This means the club needs to sell at least 700 candy bars to achieve their goal of making at least $1000 in profit.

Now, the club bought 725 bars, so selling 725 bars is sufficient as it exceeds the 700 candy bars needed.

Therefore, the correct representation of the situation is: \[ 2b - 400 \geq 1000 \quad \text{and yes, it is a viable option.} \]

Thus the best answer choice is: \[ \text{$2b - 400} \geqslant 1000, \text{ and yes, it is a viable option.} \]