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# Calculate tax and tip on your bill, assuming that tax is 8.875% and customary tip is 18%.

How do you solve this?

### 4 Answers by Expert Tutors

Ed F. | Serving you in Computer Programming, Microsoft Office, and moreServing you in Computer Programming, Mic...
4.9 4.9 (19 lesson ratings) (19)
1
You have stated that the tax rate is 8.875% and the customary tip is 18%.

To set up fomulas to figure each component, we could do the following:

b is the amount billed
x t is the tax
p is the tip
t is the total amount due

With these definitions, we can figure out each component and add the totals together.  Note, the percentage is divided by 100 to get is decimal value.

x = b * 0.08875
p = b * 0.18
t = b + x + p

So, with a bill of \$28,
x = 28 * 0.08875 = 2.485 = 2.49 (rounded to nearest penny)
p = 28 * 0.18 = 5.04
t = 28 + 2.49 + 5.04 = \$35.53

We might notice that each component is calculated from the amount due (b), which would allow us to simplify the expression by combining the like terms.  Since "t = b+x+p" is the bill plus tax and tip, we could setup the formula like this:

t = b + (b * 0.08875) + (b * 0.18)

Then we can simplify it:
t = b + 0.08875b + 0.18b
t = 1.26875b

Now plugging the \$28 of the amount due on the bill, we can calculate the total amount due including the tax and tip.
t = 1.26875 * 28 = 35.525 = \$35.53 (round up to the next penny)

Either way we will arrive at the same answer.

From the practical application side, we might notice that the tip (18%) is just over twice (2x) the tax (8.875%).  Since the amount of the tax is listed on the bill, a simple solution is to double the tax and then round up.  So if the bill before tax is \$28 and the tax added is \$2.49 (bringing the bill to \$30.49 before tip), then doubling the amount of the tax gets us \$4.98.  We can round that to \$5.  This would make the bill \$35.49, just \$0.04 under the \$35.53 of an exact calculation.  At that point we might round up to \$35.50 or even \$36, which means the server gets a little extra in the tip.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Salma;
I can only speak for myself.
When I tip, such as in a restaurant or beauty parlor, I calculate the tip amount based on the pre-tax amount.
For example,
I had a hair-cut for \$20.00.
I would tip for (\$20.00)(0.18)=\$3.60
I would be charged tax of (\$20.00)(0.08875)=\$1.78
My total bill would be...
\$20.00
\$1.78 tax
\$21.78 total to hair salon
\$3.60 tip
\$25.38 total bill

Richard L. | Engineer Tutor - Physics, Calculus, and Pre-CalculusEngineer Tutor - Physics, Calculus, and ...
4.7 4.7 (3 lesson ratings) (3)
1
Let's say your bill is \$25.00
With tax, you would pay the \$25.00 plus 8.875% of \$25.00.
\$25.00 +(8.875/100)*\$25.00 = \$27.22

Repeat with another 18% for the \$27.22 (assuming you pay tip on the taxes too).
\$27.22 + (18/100)*\$27.22 = \$32.12
Sky W. | Patient and Knowledgeable Math TutorPatient and Knowledgeable Math Tutor
5.0 5.0 (12 lesson ratings) (12)
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