SOLUTION: Luke is 2 years younger than his friend. Five years ago, Luke was three-fifths of his friends age. How old is Luke now?

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)
------
Substitute for "L" and solve for "F"::
F-2-5 = (3/5)F - 3
-------
F-7 = (3/5)F - 3
----
F-4 = (3/5)F
(2/5)F = 4
F = 10 yrs
---
Ans: Luke = F-2 = 8 yrs old
---------------
Cheers,
Stan H.
-----------
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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.

So their present ages are 8 and 10.
RELATED QUESTIONS
Mr. Smith is 81 years older than his grandson Luke. In 3 years, Mr. Smith will be four... (answered by Boreal)
c) Luke is 5 years older than twice his younger brother Thomas. If Luke is 19, how old is (answered by ikleyn)
Luke is five years younger than Jason. Two year ago, the sum of their ages was 33. How... (answered by greenestamps)
Jim is 3 years older than Pete but 2 yrs younger than Luke the sum of all there ages is... (answered by josgarithmetic,MathTherapy)
In five years, Sylvia will be twice as old as Luke. Thirteen years ago, Sylvia was three... (answered by ankor@dixie-net.com)
Luke is 5 years younger than 3 times Sydney�s age, s. In this situation, what does 3s... (answered by Theo)
jennifer is 3 years older than Luke and 2 years younger than Evan.Their total age is 44.... (answered by jorel555)
Six years ago Samuel was three fifths of his current age. How old is Samuel... (answered by ikleyn)
Luke is three times Brandon's age. The sum of four times Brandon's age and two times... (answered by Alan3354)