Roberto is having his house painted. The job takes three days, and he pays the painter the same hourly rate every day. The cost of the job is shown in the chart below.

Which of the following equations, where [tex]$h$[/tex] represents hours worked and [tex]$P$[/tex] the amount paid in dollars, represents an hourly pay rate that is greater than the painter's hourly rate?

\begin{tabular}{cccc}
& Day 1 & Day 2 & Day 3 \\
\hline Hours worked & 5 & 4 & 6 \\
Amount paid & \[tex]$300 & \$[/tex]240 & \[tex]$360 \\
\end{tabular}

Choose all answers that apply:
A. $[/tex]P = 6.5h[tex]$
B. $[/tex]P = 50h[tex]$
C. $[/tex]P = 65h[tex]$
D. $[/tex]P = 70h$



Answer :

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]