SOLUTION: Five years ago, Karma was one third as old as her father was then. In five years, Karma will be half as old as her father will be then. Find their ages now.

Question 223314: Five years ago, Karma was one third as old as her father was then. In five years, Karma will be half as old as her father will be then. Find their ages now.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let k = Karma's present age
Let f = father's present age
:
Write an equation for each statement:
:
"Five years ago, Karma was one third as old as her father was then."
k - 5 = (f - 5)
Multiply both sides by 3, results:
3(k - 5) = f - 5
3k - 15 = f - 5
3k = f - 5 + 15
3k = f + 10
:
"In five years, Karma will be half as old as her father will be then."
k + 5 = (f + 5)
Multiply both sides by 2
2(k+5) = f + 5
2k + 10 = f + 5
2k = f + 5 - 10
2k = f - 5
;
Find their ages now.
:
Take the two equations
3k = f + 10
2k = f - 5
---------------subtraction eliminates f, find k
k = 15, karma's present age
;
Find f using 3k = f + 10
3(15) = f + 10
45 - 10 = f
35 = f, father's present age
:
:
Check solution in the statement
"In five years, Karma will be half as old as her father will be then."
15 + 5 = .5(35 + 5)
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