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.

Steps to Solve

1. Identify the costs involved

From the problem, we know two costs:

• For 2 hours, the cost is $100: $$ y = c + 2h $$
• For 6 hours, the cost is $260: $$ y = c + 6h $$

Where $c$ is the travel fee and $h$ is the hourly fee.

2. Create a system of equations

We can set up two equations based on the information provided:

• For 2 hours: $$ 100 = c + 2h $$
• For 6 hours: $$ 260 = c + 6h $$

3. Solve the system of equations

Subtract the first equation from the second to eliminate $c$:

$$ (260 - 100) = (c + 6h) - (c + 2h) $$

This simplifies to:

$$ 160 = 4h $$

Now, solve for $h$:

$$ h = \frac{160}{4} = 40 $$

4. Substitute back to find ( c )

Now, substitute $h = 40$ back into the first equation:

$$ 100 = c + 2(40) $$

Calculate:

$$ 100 = c + 80 $$

Thus,

$$ c = 100 - 80 = 20 $$

5. Formulate the total cost equation

Now that we have $c$ and $h$, we can express the total cost $y$ as:

$$ y = c + hx $$ Substituting the values of $c$ and $h$, we get: $$ y = 20 + 40x $$