Question 1116799: Luke is 2 years younger than his friend. Five years ago, Luke was three-fifths of his friends age. How old is Luke now? Found 2 solutions by stanbon, greenestamps:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Luke is 2 years younger than his friend. Five years ago, Luke was three-fifths of his friends age. How old is Luke now?
Equations:
L = F - 2
L-5 = (3/5)(F-5)
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Substitute for "L" and solve for "F"::
F-2-5 = (3/5)F - 3
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F-7 = (3/5)F - 3
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F-4 = (3/5)F
(2/5)F = 4
F = 10 yrs
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Ans: Luke = F-2 = 8 yrs old
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Cheers,
Stan H.
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The algebraic solution provided by the other tutor is of course fine; and perhaps you needed to see an algebraic solution.
But you can get some good mental exercise from solving this problem using logical reasoning.
Think about it. If the difference in their ages is 2 years, and 5 years ago Luke was 3/5 of his friend's age, then their ages 5 years ago had to be 3 and 5.
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