a repair person charges a travel fee to visit a home and an hourly fee for the time spent fixing a leak. a repair that takes 2hours cost $100 a repair that takes 6hours cost $260

Question

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.

y = __x + __

Answer 1

To create an equation that represents the total cost of a repair, we need to identify the travel fee (the fixed cost) and the hourly fee (the variable cost).

Given the information:

1. If the repair takes 2 hours, the total cost is $100.
2. If the repair takes 6 hours, the total cost is $260.

We can set up a system of equations to solve for the hourly fee and the travel fee.

Let:

• $b$ be the travel fee (fixed cost),
• $p$ be the hourly fee.

From the given information, we can set up the following equations:

1. $2p+b=100$ (for 2 hours)
2. $6p+b=260$ (for 6 hours)

Now, let's subtract the first equation from the second:

$$(6p+b)-(2p+b)=260-100$$

This simplifies to:

$$4p=160$$

Dividing both sides by 4, we find:

$$p=40$$

Now that we have the hourly fee, we can substitute $p$ back into one of the original equations to find $b$:

Using $2p+b=100$:

$$2(40)+b=100$$ $$80+b=100$$ $$b=20$$

Now we have the values for both the travel fee and the hourly fee:

• Travel fee ($b$) = $20
• Hourly fee ($p$) = $40

Therefore, the equation representing the total cost of a repair $y$ as a function of the number of hours spent fixing a leak $x$ is:

$$y=40x+20$$

So in the format $\text{Missing open brace for subscript}$:

$$y=40x+20$$