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October 28th, 2009, 03:34 PM   #1
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The Math Test

Violet was taking a math test. On one problem she was given two positive whole numbers. The problem asked her to square the two numbers and add the squares together. Unforunately, Violet misinterpreted the question. She mistakenly added the two numbers first and squared the result. Her answer was 60 greater than the correct answer to the question. Find all possibilities for the orginal two numbers.
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October 28th, 2009, 03:58 PM   #2
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Re: The Math Test

Let a and b be the two numbers and let x be the value of a + b.

a + b = x

(a + b) = x + 60

Expand the left-hand side of (a + b) = x + 60:
a + 2ab + b = x + 60

Substitute x = a + b:
a + 2ab + b = a + b + 60

2ab = 60, ab = 30, so a and b are factors of 30.
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October 30th, 2009, 06:25 AM   #3
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Re: The Math Test

Can you explain why you explaned the left side?
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October 30th, 2009, 06:37 AM   #4
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Re: The Math Test

To get a + 2ab + b, which is easier to work with.
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