How do you solve this?

and explain the steps please..

How do you solve this?

and explain the steps please..

Tutors, please sign in to answer this question.

Lexington, KY

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.

Middletown, CT

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

New York, NY

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).

Berkeley Springs, WV

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.

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.

Marianna L.

GRE and SAT Tutor: Kaplan Teacher and Columbia PhD Student

New York, NY

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Kyle D.

CFA 3 Passed (Passed All CFA exams on first try), Columbia Grad

Jersey City, NJ

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