To determine which equations represent an hourly pay rate greater than the painter's hourly rate, we need to first calculate the painter's hourly rate using the given data.
Here's the data:
- Day 1: 5 hours, \[tex]$300
- Day 2: 4 hours, \$[/tex]240
- Day 3: 6 hours, \$360
### Step 1: Calculate the Total Hours Worked
The total hours worked by the painter over the three days can be calculated as:
[tex]\[ 5 + 4 + 6 = 15 \text{ hours} \][/tex]
### Step 2: Calculate the Total Amount Paid
The total amount paid to the painter over the three days can be calculated as:
[tex]\[ 300 + 240 + 360 = 900 \text{ dollars} \][/tex]
### Step 3: Calculate the Painter's Hourly Rate
The hourly rate [tex]\( r \)[/tex] can be found by dividing the total amount paid by the total hours worked:
[tex]\[ r = \frac{900}{15} = 60 \text{ dollars per hour} \][/tex]
### Step 4: Compare Each Equation's Hourly Rate to the Painter's Hourly Rate
We have four equations, each of which represents a different hourly pay rate.
1. Equation A: [tex]\( P = 6.5h \)[/tex]
- The hourly rate in this equation is [tex]\( 6.5 \)[/tex] dollars per hour.
- [tex]\( 6.5 < 60 \)[/tex], so this rate is not greater than the painter's rate.
2. Equation B: [tex]\( P = 50h \)[/tex]
- The hourly rate in this equation is [tex]\( 50 \)[/tex] dollars per hour.
- [tex]\( 50 < 60 \)[/tex], so this rate is not greater than the painter's rate.
3. Equation C: [tex]\( P = 65h \)[/tex]
- The hourly rate in this equation is [tex]\( 65 \)[/tex] dollars per hour.
- [tex]\( 65 > 60 \)[/tex], so this rate is greater than the painter's rate.
4. Equation D: [tex]\( P = 70h \)[/tex]
- The hourly rate in this equation is [tex]\( 70 \)[/tex] dollars per hour.
- [tex]\( 70 > 60 \)[/tex], so this rate is greater than the painter's rate.
### Conclusion
The equations that represent an hourly pay rate greater than the painter's hourly rate are:
- C: [tex]\( P = 65h \)[/tex]
- D: [tex]\( P = 70h \)[/tex]
Thus, the correct answers are:
- C [tex]\( P = 65h \)[/tex]
- D [tex]\( P = 70h \)[/tex]
