Checking Your Work

Date: 09/11/2003 at 07:30:36
From: Boris
Subject: Algebra, percentages, increase and decrease

The whole class including the teacher has been working on this 
problem and wasn't able to solve it. Here it is.

  The purchase price of a diamond ring increases by $20 when 
  the rate of VAT is increased from 12% to 20%. Find the 
  original price of the ring.

Here's what we tried:

  1) 20 - 12 = 8, so the VAT increased by 8%

  2) 8% of OP (original price) = $20 

     because it says that OP increased by $20, so

  3) OP * 0.08 = 20

            OP = 20/0.08

            OP = 250 

So, we come up with an original price of $250. However, the teacher's
answer book says it's $280. What did we do wrong?

Date: 09/11/2003 at 13:12:01
From: Doctor Peterson
Subject: Re: Algebra, percentages, increase and decrease

Hi, Boris.

The answer book is wrong -- or else the problem itself was copied 
wrong, which is equivalent.

You can check the book's answer. Suppose the original price was $280.
Then 12% VAT is $33.60, and 20% VAT is $56. The purchase price
increased from $313.60 to $336, an increase of $22.60, not $20.

Ah! But maybe "the original price" means "the original PURCHASE 
price". Let's take our correct answer and see what that is. The VAT 
changes from $30 to $50, an increase of $20; the purchase price 
increases from $280 to $300. And, yes, it is the original purchase 
price that they are asking for.

Sometimes English is the hardest part of math!

The lesson from this: trust your work, and check it; checking can 
often help you see what the problem means, which is the key. 
By "checking" your work only by comparing it with the answer key, 
rather than believing that your work was right and trying to prove it 
was, you missed a chance to see what was happening.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/