Let's break down this problem step by step to determine the number of hours the plumber worked.
1. Define the given values:
- The fixed charge for the plumber to come to the house is \[tex]$35.
- The charge per hour for the plumber’s work is \$[/tex]60.
- The total charge that Jerald paid is \$305.
2. Set up the equation:
- Let's denote the number of hours the plumber worked by [tex]\( x \)[/tex].
- The total charge can be expressed in an equation where the fixed charge plus the hourly charge equals the total charge.
- Therefore, the equation will be:
[tex]\[
60x + 35 = 305
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- First, isolate the term with [tex]\( x \)[/tex] on one side of the equation by subtracting the fixed charge from the total charge:
[tex]\[
60x + 35 - 35 = 305 - 35
\][/tex]
Simplifying this, we get:
[tex]\[
60x = 270
\][/tex]
- Next, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by the hourly charge:
[tex]\[
x = \frac{270}{60}
\][/tex]
- Performing the division gives us:
[tex]\[
x = 4.5
\][/tex]
4. Conclusion:
- The plumber worked for [tex]\( 4.5 \)[/tex] hours.
Hence, the equation that correctly represents the problem and its solution is:
[tex]\[
60x + 35 = 305 \quad \Rightarrow \quad x = 4.5 \text{ hours}
\][/tex]
