Question

A plumber charges a one-time visit fee and then charges on an hourly basis plus the rate for any part/material needed plus the tax on the required material value. If the total cost of completing a job takes $h$ hours is given by the function $C(h) = 45h + 1.06(82.5) + 75$, then the term $1.06(82.5)$ represents
A.The hourly rate
B.The site visit fee
C.The cost of materials, including tax
D.The cost of materials, not including tax

Answer 1

The total cost incurred can be broken down into 4 parts. One is the one-time visit fee, second is the charge on hourly basis of the work done, third is the cost of material and last is the tax on the required materials. We can easily find the nature of each term in a given function to find cost and determine that $1.06(82.5)$ indicates the cost of material, with taxes.

Complete step-by-step answer:
The total cost of completing the job is given by function $C(h) = 45h + 1.06(82.5) + 75$. Here there are three terms given $45h$, $1.06(82.5)$ and $75$.
Out of these the term $45h$ is variable and depends on the number of hours, thus this term is the charge by the plumber on an hourly basis.
Second term is $1.06(82.5)$, which is a multiple of two terms. As the plumber has a constant one-time visit fee this cannot be a one-time visit fee. It has to be the cost of materials. Also notice how the number 82.5 is multiplied with a number just greater than one, thus indicating that 1.06 is multiplied due to a tax of $6\%$.
Thus, the term $1.06(82.5)$, indicates the cost of materials, including the taxes.
Also the third term is 75, which is a constant number without any multiplication in it, so it must be the one-time visit fee of the plumber.
Hence, option (C) is the correct option.

Note: These types of questions can easily be solved on the basis of simple observation and clues given in the question. Here, for this question, the clues were ‘one-time fee’ and ‘charge on hourly basis’ which leaves us with the third and the remaining term. The function can also be reframed such that it has 4 terms where the cost of the material and tax on it can be written separately as 2 terms.