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)

Question

Responses

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 greater than or equal to 1000 , and no, it is not 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 determine which inequality represents the situation, let's establish the variables and calculations involved.

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

The profit made from selling \( b \) bars is given by revenue minus the cost:

• Revenue from selling candy bars: \( 2b \) (since each bar sells for $2)
• Total cost of the candy bars: $400

Thus, the profit can be represented as: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400 \]

The club needs to make at least $1,000 in profit: \[ 2b - 400 \geq 1000 \]

Now, let's solve this 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 candy bars to make the desired profit of $1,000.

Now, checking the viability: The club has 725 bars available. Since \( 725 \geq 700 \), selling 725 bars will indeed allow the club to reach or exceed their profit goal.

Therefore, the correct choice from the options given is: 2b − 400 ≥ 1000, and yes, it is a viable option.