Problems With Sales Tax

by Deja
(Cleavland,Ohio,USA)

The Sheng family had dinner at their favorite restaurant. A 10% sales tax was added to their bill. Amy paid the bill with a $20 gift certificate plus $23.5. How much did the family's dinner cost before tax? Round your answer to the nearest penny.

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Sep 24, 2010
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by: Karin

Let's first talk about the things that we know in this problem.

1. We know that the total bill was $43.50. Amy paid with a $20 gift certificate, plus 23.50. (20+23.50 = 43.50)

2. We know that 10% sales tax was added to the bill. We know that we must convert the % to a decimal and round it to the pre-tax total.

The question is, "What is the pre-tax total? Or How much was the original bill?"

We will need to write an equation and solve.

Let's first write the equation in words:

Original bill + 10% tax = Total

We'll let the original bill = x since we don't know that total.

Original bill + 10% tax = Total
x + .1x = 43.50

(Remember that for tax you multiply the decimal times the original amount)

Now we need to combine like terms. (1x + .1x = 1.1x)

1.1x = 43.50

Now we will divide both sides by 1.1

1.1x/1.1 = 43.5/1.1

x = 39.55

The original bill was $39.55

Now let's check to see if this is correct.

39.55 + 39.55(.10) =
39.55 + 3.96 = 43.51

Due to rounding issues, we are 1 penny off, but this is the correct answer.

I hope this helps,
Karin

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