Question

Mr. Carr is hiring a plumber to repair his sink. The cost of Plumber T is shown in the table.

A table titled Plumber T Costs is shown. It has three columns and two rows. Row one is labeled Hours, h. Row two is labeled Cost, c. One hour, one hundred twenty-eight dollars. Two hours, two hundred fifteen dollars. Three hours, three hundred two dollars.

Part A. What is the initial cost and hourly rate of Plumber T?

Part B. Write an equation to represent the function shown in the table.

Part C. Plumber W charges $95 per hour and an additional $32 for parts. What is the difference in cost between Plumber W and Plumber T if the repair takes 5 hours?

Enter the correct answers in the boxes.

Answer 1

Part A: Initial cost = $41, Hourly rate = $87.

Part B: Cost function for Plumber T is c = 87h + 41.

Part C: Plumber T is $31 cheaper than Plumber W for a 5-hour repair.

Step-by-step explanation:

Part A:

To find the initial cost and hourly rate of Plumber T, we can use the information from the table. The cost appears to be a linear function of the hours. The general form of a linear equation is y = mx + b, where y is the cost, x is the number of hours, m is the hourly rate, and b is the initial cost.

Let's use the given points (1, $128) and (2, $215) from the table to form a system of equations:

Equation 1:
`\(128 = 1 \cdot m + b\)`

Equation 2:
`\(215 = 2 \cdot m + b\)`

Subtracting Equation 1 from Equation 2:

`\[(215 - 128) = 2 \cdot m + b - (1 \cdot m + b)\]\[87 = 1 \cdot m\]`

So, the hourly rate (m) is $87

Now, substitute the value of m back into Equation 1 or 2 to find b:

`\[128 = 1 \cdot 87 + b\]`

b = 41

Therefore, the initial cost (b) is $41, and the hourly rate (m) is $87. The equation representing Plumber T's cost function is c = 87h + 41.

Part B:

The equation representing the function shown in the table is c = 87h + 41.

Part C:

Plumber W's cost function is
`\(c_w = 95h + 32\)`, where
`\(c_w\)` is the cost and h is the number of hours.

If the repair takes 5 hours, let's calculate the cost for both plumbers:

For Plumber T:

`\[c_t = 87 \cdot 5 + 41 = 435 + 41 = 476\]`

For Plumber W:

`\[c_w = 95 \cdot 5 + 32 = 475 + 32 = 507\]`

The difference in cost between Plumber W and Plumber T for a 5-hour repair is 507 - 476 = 31. Therefore, Plumber T is $31 cheaper than Plumber W for a 5-hour repair.

The probable question can be: Mr. Carr is hiring a plumber to repair his sink. The cost of Plumber T is shown in the table.

Plumber T Costs

Hours, h

1

2

3

Cost, c

$128

$215

$302

Part A

What is the initial cost and hourly rate of Plumber T?

initial cost = rate per hour =

Part B

Write an equation to represent the function shown in the table.

Part C

Plumber W charges $95 per hour and an additional $32 for parts. What is the difference in cost between Plumber W and Plumber T if the repair takes 5 hours?