Let's carefully analyze the situation and determine how many driveways Paula shoveled on Sunday, supported by the correct equation.
Step 1: Understand the Problem
- Paula charges \[tex]$12 per driveway.
- She shoveled 6 driveways on Saturday.
- She earned a total of \$[/tex]144 over the weekend, which includes both Saturday and Sunday earnings.
Step 2: Formulate the Equation
Let's denote the number of driveways Paula shoveled on Sunday as [tex]\( x \)[/tex].
From the problem statement:
- On Saturday, Paula shoveled 6 driveways:
- Earnings for Saturday = [tex]\( 6 \text{ driveways} \times 12 \text{ dollars per driveway} = 72 \text{ dollars} \)[/tex]
- Paula's total earnings over the weekend (Saturday + Sunday) = 144 dollars.
Thus, the equation to represent the total earnings over the weekend, taking into account the driveways shoveled on both days, would be:
[tex]\[ 12 \times (\text{driveways on Saturday} + \text{driveways on Sunday}) = 144 \][/tex]
[tex]\[ 12 \times (6 + x) = 144 \][/tex]
So, the correct equation is:
[tex]\[ \boxed{12(6 + x) = 144} \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Now, solve the equation for [tex]\( x \)[/tex]:
[tex]\[ 12(6 + x) = 144 \][/tex]
- Expand the left-hand side:
[tex]\[ 12 \times 6 + 12 \times x = 144 \][/tex]
[tex]\[ 72 + 12x = 144 \][/tex]
- Isolate [tex]\( x \)[/tex]:
[tex]\[ 12x = 144 - 72 \][/tex]
[tex]\[ 12x = 72 \][/tex]
[tex]\[ x = \frac{72}{12} \][/tex]
[tex]\[ x = 6 \][/tex]
So, Paula shoveled [tex]\(\boxed{6}\)[/tex] driveways on Sunday.
Conclusion:
Based on the analysis, we select:
- The correct equation: [tex]\(12(6 + x) = 144\)[/tex]
- The correct number of driveways shovelled on Sunday: 6 driveways
So, the correct answers are:
- C. Equation: [tex]\( 12(6 + x) = 144 \)[/tex]
- B. Answer: 6 driveways
Thus, Paula shoveled 6 driveways on Sunday.
