Jerald is having drain issues at his home and decides to call a plumber. The plumber charges [tex]$\$[/tex]35[tex]$ to come to his house and $[/tex]\[tex]$60$[/tex] for every hour they work. If the plumber charges Jerald a total of [tex]$\$[/tex]305[tex]$, how many hours did the plumber work?

Write and solve an equation to determine the number of hours worked by the plumber.

A. $[/tex]35 + 60x = 305; \quad x = 4.5[tex]$ hours
B. $[/tex]35x - 60 = 305; \quad x = 10.4[tex]$ hours
C. $[/tex]60x + 35 = 305; \quad x = 4.5[tex]$ hours
D. $[/tex]60x - 35 = 305; \quad x = 5.7$ hours



Answer :

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]