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 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 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.
Responses
1.50r+49.75≥120
, and selling 10 dozen roses is viable.
1.50 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 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.
Answers
GPT-4o mini
To determine if Seneca and her Scout troop can make a profit of at least $120 from selling the roses, we start by analyzing the costs and profits involved.
1. **Understanding the costs:**
- They bought 10 dozen roses. Since there are 12 roses in a dozen:
\[
10 \text{ dozen} = 10 \times 12 = 120 \text{ roses}
\]
- The total cost for the 10 dozen roses is $49.75.
2. **Selling price:**
- They will be selling each rose for $1.50.
- If they sell all 120 roses, their total revenue (R) from selling the roses will be:
\[
R = 1.50 \times 120 = 180 \text{ dollars}
\]
3. **Profit calculation:**
- Profit (P) can be calculated by subtracting the total cost from the total revenue:
\[
P = R - \text{Total Cost} = 180 - 49.75 = 130.25 \text{ dollars}
\]
4. **Setting up the inequality:**
- To check if the profit is at least $120, we set up the inequality based on the profit:
\[
R - 49.75 \geq 120
\]
- Replacing R with the selling price per rose times the number of roses (r = 120):
\[
1.50(120) - 49.75 \geq 120
\]
- This can be simplified. But we can also write a more general inequality for any number of roses sold (r):
\[
1.50r - 49.75 \geq 120
\]
- This relates the number of roses sold (r) to the requirement of a minimum profit.
5. **Checking the solution:**
- Now we can calculate whether \( r = 120 \) satisfies this inequality:
\[
1.50(120) - 49.75 \geq 120
\]
\[
180 - 49.75 \geq 120
\]
\[
130.25 \geq 120 \quad \text{(This is TRUE)}
\]
Therefore, the correct inequality to represent this situation is:
\[
1.50r - 49.75 \geq 120
\]
And since \( r = 120 \) leads to a profit greater than $120, selling 10 dozen roses is indeed viable.
The correct response is:
**1.50r−49.75≥120, and selling 10 dozen roses is viable.**
1. **Understanding the costs:**
- They bought 10 dozen roses. Since there are 12 roses in a dozen:
\[
10 \text{ dozen} = 10 \times 12 = 120 \text{ roses}
\]
- The total cost for the 10 dozen roses is $49.75.
2. **Selling price:**
- They will be selling each rose for $1.50.
- If they sell all 120 roses, their total revenue (R) from selling the roses will be:
\[
R = 1.50 \times 120 = 180 \text{ dollars}
\]
3. **Profit calculation:**
- Profit (P) can be calculated by subtracting the total cost from the total revenue:
\[
P = R - \text{Total Cost} = 180 - 49.75 = 130.25 \text{ dollars}
\]
4. **Setting up the inequality:**
- To check if the profit is at least $120, we set up the inequality based on the profit:
\[
R - 49.75 \geq 120
\]
- Replacing R with the selling price per rose times the number of roses (r = 120):
\[
1.50(120) - 49.75 \geq 120
\]
- This can be simplified. But we can also write a more general inequality for any number of roses sold (r):
\[
1.50r - 49.75 \geq 120
\]
- This relates the number of roses sold (r) to the requirement of a minimum profit.
5. **Checking the solution:**
- Now we can calculate whether \( r = 120 \) satisfies this inequality:
\[
1.50(120) - 49.75 \geq 120
\]
\[
180 - 49.75 \geq 120
\]
\[
130.25 \geq 120 \quad \text{(This is TRUE)}
\]
Therefore, the correct inequality to represent this situation is:
\[
1.50r - 49.75 \geq 120
\]
And since \( r = 120 \) leads to a profit greater than $120, selling 10 dozen roses is indeed viable.
The correct response is:
**1.50r−49.75≥120, and selling 10 dozen roses is viable.**