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Question 118139: A wealthy old man is criticized for marrying a woman for he is three times her age. He wittily replies ,"h, but in 20 years time 2 shall only be twice her age." How old is the man and his wife?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let W represent the wife's present age and M represent the man's present age.
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At the present time the man is 3 times as old as his wife. So 3 times the wife's age equals the
man's age. In equation form this is:
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3W = M
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20 years from now the wife will be W + 20 years old and the man will be M + 20 years old.
You are told that at that time the man's age will equal twice that of his wife's age. In
equation form this is:
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2(W + 20) = M + 20
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Multiply out the left side of this second equation and you get:
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2W + 40 = M + 20
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Get rid of the 40 on the left side by subtracting 40 from both sides to get:
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2W = M - 20
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And get rid of the M on the right side by subtracting M from both sides. When you do that
subtraction the equation becomes:
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2W - M = -20
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But the very first equation told us that M = 3W. So in this latest equation we can substitute
3W for M to get:
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2W - 3W = -20
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Do the subtraction on the left side. 2W minus 3W equals -W so the equation becomes:
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-W = -20
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Multiply both sides of this equation by -1 and it becomes:
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W = 20
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Since W is the wife's current age, we know that at this time the wife is 20 years old.
And since the man is presently 3 times as old as his wife, he has to be 60.
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As a check, if the wife is currently 20, in 20 years from now she will be 40. And since
the man is currently 60 years old, in 20 years he will be 80. At that time will he be
twice as old as his wife ... is 80 twice as old as 40? Yes it is, so the answers check.
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The wife is now 20 and her husband is 60.
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Hope this helps you to understand the problem and how to solve it.
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Have a happy new year!
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