Question

Question

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

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.

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.

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.

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

Answer 1

To solve this problem, we first need to establish the total profit the club needs to make. The club needs to make at least $1,000 for their trip, and they spent $400 to buy the candy bars.

Let \( b \) represent the number of candy bars sold.

The revenue from selling \( b \) candy bars at $2 each would be \( 2b \). The profit, which is the revenue minus the cost, can be expressed as:

\[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

To find the inequality for the profit needed, we set it up as follows:

\[ 2b - 400 \geq 1000 \]

Now, let's solve for \( b \) to see how many candy bars the club needs to sell:

1. Add 400 to both sides: \[ 2b \geq 1400 \]

2. Divide by 2: \[ b \geq 700 \]

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

Since they have 725 bars, they can indeed sell enough to meet their goal. Therefore, they have a viable option.

The correct response is:

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