Question

How would I solve this question? A plumbing company charges $75 per hour with a $100 inspection fee. A sales tax of 8.25% is thencalculated based on the charges (subtotal). How much would the total charge be for 3 hours of service?

Answer 1

Given

A plumbing company charges $75 per hour with a $100 inspection fee.

A sales tax of 8.25% is then calculated based on the charges (subtotal).

To find:

How much would the total charge be for 3 hours of service?

Explanation:

It is given that,

A plumbing company charges $75 per hour with a $100 inspection fee.

And, a sales tax of 8.25% is then calculated based on the charges (subtotal).

Then,

The cost of job which takes h hours is,

$c(h)=75h+100$

And, the sales tax bases on the charges of h hours is,

$\begin{gathered} s(c(h))=s(75h+100) \\ =0.0825(75h+100) \end{gathered}$

Therefore, the total charge for h hours of service is,

$\begin{gathered} t(h)=c(h)+s(c(h)) \\ =(75h+100)+0.0825(75h+100) \\ =(75h+100)(1+0.0825) \\ =(75h+100)(1.0825) \end{gathered}$

Then, for h=3,

$\begin{gathered} t(3)=(75\times3+100)(1.0825) \\ =(225+100)(1.0825) \\ =325\times1.0825 \\ =351.8125 \\ =351.8 \end{gathered}$

Hence, the total charge for 3 hours of service is $351.8.