Question
Seneca and her Scout troop bought 10 dozen roses for $49.75. They are selling each rose for $1.50. Will they be able to make a profit of at least $120 for their upcoming trip? Find the inequality to represent this situation and determine if the solution is viable.(1 point)
Responses
1.50r−49.75≥120
, and selling 10 dozen roses is viable.
1.50 r minus 49.75 greater than or equal to 120 , and selling 10 dozen roses is viable.
10r+49.75≥120
, and selling 10 dozen roses is viable.
10 r plus 49.75 greater than or equal to 120 , and selling 10 dozen roses is viable.
1.50r−49.75≥120
, and selling 10 dozen roses is not viable.
1.50 r minus 49.75 greater than or equal to 120 , and selling 10 dozen roses is not viable.
1.50r+49.75≥120
, and selling 10 dozen roses is viable.
Responses
1.50r−49.75≥120
, and selling 10 dozen roses is viable.
1.50 r minus 49.75 greater than or equal to 120 , and selling 10 dozen roses is viable.
10r+49.75≥120
, and selling 10 dozen roses is viable.
10 r plus 49.75 greater than or equal to 120 , and selling 10 dozen roses is viable.
1.50r−49.75≥120
, and selling 10 dozen roses is not viable.
1.50 r minus 49.75 greater than or equal to 120 , and selling 10 dozen roses is not viable.
1.50r+49.75≥120
, and selling 10 dozen roses is viable.
Answers
GPT-4o mini
To determine whether Seneca and her Scout troop can make at least $120 in profit from selling 10 dozen roses, let's break down the situation:
1. **Cost of the roses**: They bought 10 dozen roses. Since there are 12 roses in a dozen, they have:
\[
10 \text{ dozen} \times 12 \text{ roses/dozen} = 120 \text{ roses}
\]
2. **Total cost**: The cost for 10 dozen roses is $49.75.
3. **Selling price**: They are selling each rose for $1.50. Therefore, the total revenue (R) from selling all roses is:
\[
R = \text{(number of roses)} \times \text{(price per rose)} = 120 \text{ roses} \times 1.50 \text{ dollars/rose} = 180 \text{ dollars}
\]
4. **Profit calculation**: Profit (P) can be calculated by subtracting the total cost from the total revenue:
\[
P = R - \text{Cost} = 180 - 49.75 = 130.25
\]
5. **Inequality to represent the situation**: They want to check if the profit is at least $120. This leads to the inequality:
\[
1.50r - 49.75 \geq 120
\]
where \( r \) is the number of roses they sell (in this case, \( r = 120 \)).
Now plug in \( r \) (the total number of roses, which is 120):
\[
1.50(120) - 49.75 \geq 120
\]
This simplifies to:
\[
180 - 49.75 \geq 120
\]
\[
130.25 \geq 120
\]
This statement is true.
**Conclusion**: Selling 10 dozen roses with the given conditions will allow them to make a profit of at least $120.
So, the correct response is:
**1.50r − 49.75 ≥ 120, and selling 10 dozen roses is viable.**
1. **Cost of the roses**: They bought 10 dozen roses. Since there are 12 roses in a dozen, they have:
\[
10 \text{ dozen} \times 12 \text{ roses/dozen} = 120 \text{ roses}
\]
2. **Total cost**: The cost for 10 dozen roses is $49.75.
3. **Selling price**: They are selling each rose for $1.50. Therefore, the total revenue (R) from selling all roses is:
\[
R = \text{(number of roses)} \times \text{(price per rose)} = 120 \text{ roses} \times 1.50 \text{ dollars/rose} = 180 \text{ dollars}
\]
4. **Profit calculation**: Profit (P) can be calculated by subtracting the total cost from the total revenue:
\[
P = R - \text{Cost} = 180 - 49.75 = 130.25
\]
5. **Inequality to represent the situation**: They want to check if the profit is at least $120. This leads to the inequality:
\[
1.50r - 49.75 \geq 120
\]
where \( r \) is the number of roses they sell (in this case, \( r = 120 \)).
Now plug in \( r \) (the total number of roses, which is 120):
\[
1.50(120) - 49.75 \geq 120
\]
This simplifies to:
\[
180 - 49.75 \geq 120
\]
\[
130.25 \geq 120
\]
This statement is true.
**Conclusion**: Selling 10 dozen roses with the given conditions will allow them to make a profit of at least $120.
So, the correct response is:
**1.50r − 49.75 ≥ 120, and selling 10 dozen roses is viable.**