Question

The adventure club is selling candy bars to go on their annual outing. The bars sell $2 a bar The club bought 725 bars for $400The 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) 2b - 400 < 1000 and noit is not a viable option 2b - 400 >= 1000 and yes, it is a viable option 2b - 400 <= 1000 and yes, it is a viable option 2b - 400 > 100% and noit is not a viable option

Answer 1

To define the inequality that represents the problem, we need to consider the revenue generated from selling the candy bars and the cost incurred.

1. Selling price per bar: $2
2. Number of bars: 725
3. Cost of buying the bars: $400
4. Minimum profit needed: $1,000

To find the inequality, we start by calculating the revenue from selling the bars:

• Revenue from selling \( b \) bars = \( 2b \)

Next, we need to calculate the profit:

• Profit = Revenue - Cost
• Profit = \( 2b - 400 \)

The club needs to make at least $1,000 in profit, so we set up the inequality:

\[ 2b - 400 \geq 1000 \]

Now, we solve the inequality for \( b \):

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

This means the club needs to sell at least 700 bars to make a profit of at least $1,000.

Now, let's check if selling 725 bars will yield enough profit:

Calculate the profit if 725 bars are sold:

\[ \text{Profit} = 2(725) - 400 \] \[ \text{Profit} = 1450 - 400 = 1050 \]

Since $1050 is greater than $1000, selling 725 bars is indeed a viable option.

So, the correct choice is: \[ 2b - 400 \geq 1000 \quad \text{and yes, it is a viable option} \]