A repair person charges a travel fee to visit a home and an hourly fee for time spent fixing a leak. A repair person that takes 2h charges $100. A repair that takes 6h cost $260. Write an equation to represent the total cost of a repair,y, as a function of the number of hours spent fixing a leak ,x.

Answer 1

To create an equation that represents the total cost of a repair, $y$, as a function of the number of hours spent fixing a leak, $x$, we need to identify the components of the cost.

We know from the problem:

1. A repair person charges a travel fee (let's call it $F$) and an hourly fee (let's call it $H$) for the work done.
2. From the first scenario, where the total cost for 2 hours is $100, we can write the equation: $$F+2H=100$$
3. From the second scenario, where the total cost for 6 hours is $260, we can write the second equation: $$F+6H=260$$

Now, we can solve this system of equations to find the values of $F$ and $H$.

Step 1: Subtract the first equation from the second equation to eliminate $F$: $$(F+6H)-(F+2H)=260-100$$ This simplifies to: $$4H=160$$ So, $$H=40$$

Step 2: Substitute $H$ back into one of the original equations to solve for $F$. We can use the first equation: $$F+2(40)=100$$ $$F+80=100$$ $$F=20$$

Now that we have $F=20$ and $H=40$, we can express the total cost $y$ as a function of the number of hours $x$:

The total cost $y$ can be represented by the equation: $$y=F+Hx$$ Substituting the values of $F$ and $H$: $$y=20+40x$$

Thus, the equation representing the total cost of a repair $y$ as a function of the number of hours spent fixing a leak $x$ is: $$y=20+40x$$