Question 223314
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 = {{{1/3}}}(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 = {{{1/2}}}(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)