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Question
The sale tax on a particular article is $3.12 . If the rate of sales tax is 6.5%, what was the price of this article?

- First off, to make it easier for both of us, I think that it is basically asking what the "regular" price of the article was, correct?

- Second, my answer that I got was $3.34, and my friend got $3.32 . Are any of the two answers correct? If not, could you please answer and give the steps to solve for this question? Thanks.

Answer
Hey! Glad to see you working out the problems. For your first question, it does refer to the regular price of the article. I can see how it could be confusing since the word "sales" can refer to an item that is on "sale", that is, being sold at a reduced price. In this case however the tax is on the (regular) price they are selling it at.

For the calculation, the rerlationships are similar to your previous problems, that is

(amount of sales tax = S) = (price of article = P) x (sales tax rate = R), or symbolically

S = P R.

This can be arranged by very simple algebra to give the equivalent expression for the quantity you are after

P = S/R = (3.12)/(0.065) = $48.

Note that I have converted the percentage sales tax rate to a factor; 6.5% -> 0.065 (how?).

You and your friend gave it a good try but didn't get the sequence quite right. You calculated 6.5% of $3.12 and added it to $3.12. This would be written as

answer = SR + S,

which you can see isn't right compared to the equation above. Note also that, for a small percentage like 6.5%, the amount of tax will be much smaller than the price of the article. In the same sense, the price of the article (which is what you are solving for in this problem) should be much larger than the amount of sales tax. This is a good mental check on your calculations.

Hang in there.

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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