Question
Richard is going to have the exterior of his home painted. He will choose between Premium Painting, Inc. and Bulldog Painting. Premium Painting, Inc. charges $150.00 to come out and evaluate the house plus $10.00 for every additional 30 minutes of work. Bulldog Painting charges $25.00 per hour of work. Let h represent the number of hours for which Richard hires a painter. Which of the following statements are true?
Select all that apply.
Responses
If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper.
If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper. EndFragment
The expression 20h represents the total charge for Premium Painting, Inc.
The expression 20h represents the total charge for Premium Painting, Inc. EndFragment
The expression 150+20h+25h represents the total amount Richard will spend on the painters to paint the exterior of his home.
The expression 150+20h+25h represents the total amount Richard will spend on the painters to paint the exterior of his home. EndFragment
The expression 25h represents the total charge for Bulldog Painting.
StartFragment The expression 25h represents the total charge for Bulldog Painting.
If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper.
If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper. EndFragment
Select all that apply.
Responses
If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper.
If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper. EndFragment
The expression 20h represents the total charge for Premium Painting, Inc.
The expression 20h represents the total charge for Premium Painting, Inc. EndFragment
The expression 150+20h+25h represents the total amount Richard will spend on the painters to paint the exterior of his home.
The expression 150+20h+25h represents the total amount Richard will spend on the painters to paint the exterior of his home. EndFragment
The expression 25h represents the total charge for Bulldog Painting.
StartFragment The expression 25h represents the total charge for Bulldog Painting.
If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper.
If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper. EndFragment
Answers
GPT-4o mini
Let's analyze each statement one by one to determine their validity.
1. **If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper.**
For Premium Painting, Inc.:
- Evaluation fee: $150
- Charge: $10 per 30 minutes = $20 per hour
- Total cost for 10 hours = $150 + (20 * 10) = $150 + $200 = $350
For Bulldog Painting:
- Charge: $25 per hour
- Total cost for 10 hours = $25 * 10 = $250
Since $250 (Bulldog) < $350 (Premium), this statement is **true**.
2. **The expression 20h represents the total charge for Premium Painting, Inc.**
The charge for Premium Painting consists of a base fee of $150 and then $20 for each hour of work (not just $20h). Therefore, the total charge cannot be expressed simply as 20h. This statement is **false**.
3. **The expression 150+20h+25h represents the total amount Richard will spend on the painters to paint the exterior of his home.**
The correct expression for the total cost would be the cost of Premium (around $150 + 20h) plus the cost of Bulldog (25h). However, for one painter only, this expression is not correct. Therefore, this statement is **false**.
4. **The expression 25h represents the total charge for Bulldog Painting.**
This statement is **true** as Bulldog Painting charges $25 per hour, so for h hours, the total charge is correctly represented as 25h.
5. **If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper.**
For Premium Painting, Inc.:
- Total cost for 40 hours = $150 + (20 * 40) = $150 + $800 = $950
For Bulldog Painting:
- Total cost for 40 hours = $25 * 40 = $1000
Since $950 (Premium) < $1000 (Bulldog), this statement is **true**.
Now, summarizing the valid statements:
- The first statement is **true**.
- The fourth statement is **true**.
- The fifth statement is **true**.
So the true statements are:
- If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper.
- The expression 25h represents the total charge for Bulldog Painting.
- If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper.
1. **If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper.**
For Premium Painting, Inc.:
- Evaluation fee: $150
- Charge: $10 per 30 minutes = $20 per hour
- Total cost for 10 hours = $150 + (20 * 10) = $150 + $200 = $350
For Bulldog Painting:
- Charge: $25 per hour
- Total cost for 10 hours = $25 * 10 = $250
Since $250 (Bulldog) < $350 (Premium), this statement is **true**.
2. **The expression 20h represents the total charge for Premium Painting, Inc.**
The charge for Premium Painting consists of a base fee of $150 and then $20 for each hour of work (not just $20h). Therefore, the total charge cannot be expressed simply as 20h. This statement is **false**.
3. **The expression 150+20h+25h represents the total amount Richard will spend on the painters to paint the exterior of his home.**
The correct expression for the total cost would be the cost of Premium (around $150 + 20h) plus the cost of Bulldog (25h). However, for one painter only, this expression is not correct. Therefore, this statement is **false**.
4. **The expression 25h represents the total charge for Bulldog Painting.**
This statement is **true** as Bulldog Painting charges $25 per hour, so for h hours, the total charge is correctly represented as 25h.
5. **If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper.**
For Premium Painting, Inc.:
- Total cost for 40 hours = $150 + (20 * 40) = $150 + $800 = $950
For Bulldog Painting:
- Total cost for 40 hours = $25 * 40 = $1000
Since $950 (Premium) < $1000 (Bulldog), this statement is **true**.
Now, summarizing the valid statements:
- The first statement is **true**.
- The fourth statement is **true**.
- The fifth statement is **true**.
So the true statements are:
- If Richard hires the painters for 10 hours, then Bulldog Painting will be cheaper.
- The expression 25h represents the total charge for Bulldog Painting.
- If Richard hires the painters for 40 hours, then Premium Painting, Inc. will be cheaper.