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
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 viable.
1.50 r minus 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 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.
Remaining Attempts : 3
Responses
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 viable.
1.50 r minus 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 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.
Remaining Attempts : 3
Answers
GPT-4o mini
To determine if Seneca and her Scout troop can make at least $120 profit from selling the roses, we first identify the cost and revenue involved.
1. **Total Cost**: They bought 10 dozen roses for $49.75. Since 1 dozen equals 12 roses, they bought:
\[
10 \text{ dozen} \times 12 \text{ roses/dozen} = 120 \text{ roses}
\]
Thus, the total cost is $49.75.
2. **Selling Price**: They are selling each rose for $1.50. If they sell all 120 roses, the revenue from selling the roses is:
\[
1.50 \text{ dollars/rose} \times 120 \text{ roses} = 180 \text{ dollars}
\]
3. **Profit Calculation**: Profit is calculated as:
\[
\text{Profit} = \text{Revenue} - \text{Cost}
\]
To make a profit of at least $120, we can set up the equation as:
\[
1.50r - 49.75 \geq 120
\]
where \( r \) is the number of roses sold (120 roses).
4. **Forming the Inequality**: Therefore, the inequality representing the situation is:
\[
1.50r - 49.75 \geq 120
\]
5. **Checking Viability**: Now, substituting \( r = 120 \) into the inequality:
\[
1.50(120) - 49.75 \geq 120
\]
\[
180 - 49.75 \geq 120
\]
\[
130.25 \geq 120
\]
This statement is true.
So we can conclude that:
- The correct inequality is: **1.50r − 49.75 ≥ 120**
- And selling 10 dozen roses is viable.
Therefore, the right response is:
**1.50r − 49.75 ≥ 120, and selling 10 dozen roses is viable.**
1. **Total Cost**: They bought 10 dozen roses for $49.75. Since 1 dozen equals 12 roses, they bought:
\[
10 \text{ dozen} \times 12 \text{ roses/dozen} = 120 \text{ roses}
\]
Thus, the total cost is $49.75.
2. **Selling Price**: They are selling each rose for $1.50. If they sell all 120 roses, the revenue from selling the roses is:
\[
1.50 \text{ dollars/rose} \times 120 \text{ roses} = 180 \text{ dollars}
\]
3. **Profit Calculation**: Profit is calculated as:
\[
\text{Profit} = \text{Revenue} - \text{Cost}
\]
To make a profit of at least $120, we can set up the equation as:
\[
1.50r - 49.75 \geq 120
\]
where \( r \) is the number of roses sold (120 roses).
4. **Forming the Inequality**: Therefore, the inequality representing the situation is:
\[
1.50r - 49.75 \geq 120
\]
5. **Checking Viability**: Now, substituting \( r = 120 \) into the inequality:
\[
1.50(120) - 49.75 \geq 120
\]
\[
180 - 49.75 \geq 120
\]
\[
130.25 \geq 120
\]
This statement is true.
So we can conclude that:
- The correct inequality is: **1.50r − 49.75 ≥ 120**
- And selling 10 dozen roses is viable.
Therefore, the right response is:
**1.50r − 49.75 ≥ 120, and selling 10 dozen roses is viable.**