Sum Twice the DifferenceDate: 10/18/2002 at 06:41:15 From: Jamie Subject: Math What number can you add to and subtract from 129 such that the sum is twice the difference? Date: 10/18/2002 at 12:36:21 From: Doctor Peterson Subject: Re: Math Hi, Jamie. We could do this using algebra, if you know any; but let's just think about what's happening, and look for an easy way to solve it. Suppose we compare the sum and difference of any two numbers; I'll add 5 to and subtract 5 from 12: 12 + 5 = 17 12 - 5 = 7 You can see that the two numbers we get differ by 10. Can you see where the 10 comes from? 0 7 12 17 +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--> |<-------------|------------->| 5 5 Now, in order for one to be twice the other, the difference (10 in this case) would have to be equal to the smaller of the two numbers (the 7 here). So we want to find a number "x" to add and subtract so that it looks like this: 0 dif 129 sum +----------------------------------------+-----------------> |<------------|------------>| x x \________________________/ \_________________________/ with the two big marked distances the same. Can you see a way to figure out how to do this? 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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