To solve the problem, let's start by rewriting the given expression using the Distributive Property. The given expression for the tax a plumber must charge is:
[tex]\[ 0.06(35 + 25h) \][/tex]
Step 1: Apply the Distributive Property
The Distributive Property states that [tex]\( a(b + c) = ab + ac \)[/tex]. Using this property, we distribute [tex]\( 0.06 \)[/tex] across the terms inside the parentheses:
[tex]\[ 0.06 \cdot 35 + 0.06 \cdot 25h \][/tex]
Step 2: Perform the multiplication
Now, let's multiply:
[tex]\[ 0.06 \cdot 35 = 2.1 \][/tex]
[tex]\[ 0.06 \cdot 25h = 1.5h \][/tex]
So, the expression becomes:
[tex]\[ 2.1 + 1.5h \][/tex]
Thus, the expression [tex]\( 0.06(35 + 25h) \)[/tex] rewritten using the Distributive Property is:
[tex]\[ 2.1 + 1.5h \][/tex]
Step 3: Calculate the tax for a 5-hour job
Now, let's find out the tax for a 5-hour job by substituting [tex]\( h = 5 \)[/tex] into the expression [tex]\( 2.1 + 1.5h \)[/tex]:
[tex]\[ \text{Tax} = 2.1 + 1.5 \cdot 5 \][/tex]
[tex]\[ \text{Tax} = 2.1 + 7.5 \][/tex]
[tex]\[ \text{Tax} = 9.6 \][/tex]
The tax for a 5-hour job is [tex]\( \$9.6 \)[/tex].
Step 4: Calculate the tax for a 20-hour job
Next, we'll find out the tax for a 20-hour job by substituting [tex]\( h = 20 \)[/tex] into the expression [tex]\( 2.1 + 1.5h \)[/tex]:
[tex]\[ \text{Tax} = 2.1 + 1.5 \cdot 20 \][/tex]
[tex]\[ \text{Tax} = 2.1 + 30 \][/tex]
[tex]\[ \text{Tax} = 32.1 \][/tex]
The tax for a 20-hour job is [tex]\( \$32.1 \)[/tex].
Summary:
- The given expression [tex]\( 0.06(35 + 25h) \)[/tex] is rewritten as [tex]\( 2.1 + 1.5h \)[/tex] using the Distributive Property.
- The tax for a 5-hour job is [tex]\( \$9.6 \)[/tex].
- The tax for a 20-hour job is [tex]\( \$32.1 \)[/tex].
