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

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.

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

 

Let's say your bill is $25.00

With tax, you would pay the $25.00 plus 8.875% of $25.00.

 

Repeat with another 18% for the $27.22 (assuming you pay tip on the taxes too).

Say your bill is $34.

 

To find the TAX, change the 8.875% to .08875 (Divided by 100) now take 34*(.08875)=3.0175 rounds to 3.02
Your total bill WITH tax is 34+3.02=37.02

Now to find the TIP your should leave with 18%, change the 18% to .18 (Divided by 100 again)
Just like before take the new total-37.02 and multiply it by .18 -> 37.02*(.18)=6.6636 which is about $6.66

So if you had a bill that was $34 before taxes, and there was an 8.875% tax, and you gave an 18% tip, you would pay about $37.02 for the meal and about $6.66 for a tip.

 

 

Hope that helps.