Question 143654: Say I collect gold coins. One day, my wife asks, ‘How many do we have?’ I say, ‘If I divide the coins into two groups, then 33 times the difference between the number of coins in each group equals the difference between the squares of the two numbers.’ How many coins do we have?“
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Say I collect gold coins. One day, my wife asks, ‘How many do we have?’ I say, ‘If I divide the coins into two groups, then 33 times the difference between the number of coins in each group equals the difference between the squares of the two numbers.’ How many coins do we have?“
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Call the amt in each pile; x & y
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An equation for what it says:
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33(x-y) = x^2 - y^2
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33(x-y) = (x-y)(x+y); factor the difference of squares
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Divide both sides by (x-y) and you have:
33 = x + y
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There any number of solutions:
some examples you can check on a calc:
x=32, y=1
33(32-1) = 32^2 - 1^2
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x=23, y=10
33(23-10) = 23^2 - 10^2
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x=18, y=15
33(18-15) = 18^2 - 15^2
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