Sure, let's go through the steps to solve the problem step-by-step.
1. Identify the given values and establish the equation:
- The plumber charges a start fee of [tex]$130.
- The plumber charges $[/tex]56 per hour.
- The total bill is [tex]$214.
Let \(x\) represent the number of hours the plumber worked. The equation for the total bill can be written as:
\[
130 + 56x = 214
\]
2. Isolate the variable term by applying the subtraction property of equality:
- Subtract the start fee of $[/tex]130 from the total bill to find out how much of the bill is attributed to the hourly work.
[tex]\[
214 - 130
\][/tex]
Performing the subtraction, we get:
[tex]\[
84
\][/tex]
So the modified equation becomes:
[tex]\[
56x = 84
\][/tex]
3. Solve for [tex]\(x\)[/tex] by applying the division property of equality:
- To make the coefficient of [tex]\(x\)[/tex] equal to 1, divide both sides of the equation by 56.
[tex]\[
x = \frac{84}{56}
\][/tex]
Performing the division, we find:
[tex]\[
x = 1.5
\][/tex]
4. Interpret the result in the context of the problem:
- The plumber worked for 1.5 hours.
Therefore, your detailed step-by-step solution shows that the plumber worked for [tex]\(1.5\)[/tex] hours if the total bill is $214.
