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/
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