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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?
and explain the steps please.. 

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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)
1
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)
1
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.