QuestionA 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 2 h costs $\$ 100$ . A repair that takes 6 h costs $\$ 260$ .
Write an equation to represent the total cost of a repair, $y$ , as a function of the number of hours spent fixing a leak, $x$ .

Studdy Solution

STEP 1

1. The total cost of a repair is composed of a travel fee and an hourly fee.
2. The repair person charges a fixed travel fee regardless of the time spent.
3. The hourly fee is constant for any number of hours worked.
4. We need to find an equation that represents the total cost $y$ as a function of the number of hours $x$ .

STEP 2

1. Define the variables and set up the system of equations.
2. Solve the system of equations to find the travel fee and hourly fee.
3. Write the equation for the total cost as a function of hours.

STEP 3

Define the variables: Let $t$ be the travel fee and $h$ be the hourly fee.
Set up the system of equations based on the given information: For 2 hours: $t + 2h = 100$ For 6 hours: $t + 6h = 260$

STEP 4

Solve the system of equations to find $t$ and $h$ .
Subtract the first equation from the second to eliminate $t$ : $(t + 6h) - (t + 2h) = 260 - 100$ $4h = 160$
Divide both sides by 4 to solve for $h$ : $h = \frac{160}{4}$ $h = 40$
Substitute $h = 40$ back into the first equation to solve for $t$ : $t + 2(40) = 100$ $t + 80 = 100$ $t = 100 - 80$ $t = 20$

STEP 5

Write the equation for the total cost $y$ as a function of the number of hours $x$ : $y = t + hx$ Substitute the values of $t$ and $h$ : $y = 20 + 40x$
The equation representing the total cost as a function of hours is: $y = 40x + 20$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms