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 yes, it is a viable option.
2 b minus 400 greater 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.
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.
Responses
2b−400≥1000
, and yes, it is a viable option.
2 b minus 400 greater 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.
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.
Answers
GPT-4o mini
To determine the correct inequality and the viability of selling 725 candy bars, let's analyze the problem step-by-step:
1. **Selling Price per Candy Bar:** Each candy bar sells for $2. Therefore, if the club sells \( b \) bars, the revenue from selling these bars will be:
\[
\text{Revenue} = 2b
\]
2. **Cost of Candy Bars:** The cost of purchasing the 725 bars was $400.
3. **Profit Calculation:** The profit is calculated as revenue minus cost:
\[
\text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400
\]
4. **Profit Requirement:** The club needs to make at least $1,000 in profit to go on their trip, which gives the inequality:
\[
2b - 400 \geq 1000
\]
5. **Solving the Inequality:**
\[
2b - 400 \geq 1000
\]
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 meet their profit requirement.
6. **Evaluating the Viability with 725 Bars:** Since the club has 725 bars, and they need to sell at least 700 bars, selling 725 bars is indeed viable.
Thus, the correct response is:
**2b−400≥1000 , and yes, it is a viable option.**
1. **Selling Price per Candy Bar:** Each candy bar sells for $2. Therefore, if the club sells \( b \) bars, the revenue from selling these bars will be:
\[
\text{Revenue} = 2b
\]
2. **Cost of Candy Bars:** The cost of purchasing the 725 bars was $400.
3. **Profit Calculation:** The profit is calculated as revenue minus cost:
\[
\text{Profit} = \text{Revenue} - \text{Cost} = 2b - 400
\]
4. **Profit Requirement:** The club needs to make at least $1,000 in profit to go on their trip, which gives the inequality:
\[
2b - 400 \geq 1000
\]
5. **Solving the Inequality:**
\[
2b - 400 \geq 1000
\]
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 meet their profit requirement.
6. **Evaluating the Viability with 725 Bars:** Since the club has 725 bars, and they need to sell at least 700 bars, selling 725 bars is indeed viable.
Thus, the correct response is:
**2b−400≥1000 , and yes, it is a viable option.**