SOLUTION: Five years ago Nicole was three times as old as Rianne. Five years hence, Nicole will be twice as old as Rianne. Find their present ages.

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Question 1122872: Five years ago Nicole was three times as old as Rianne. Five years hence, Nicole will be twice as old as Rianne. Find their present ages.
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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From the condition, you have these two equations


N - 5 = 3*(R-5)        (1)    ("Five years ago Nicole was three times as old as Rianne.")
N + 5 = 2*(R+5)        (2)    ("Five years hence . . . " )


N - 5 = 3R - 15        (3)
N + 5 = 2R + 10        (4)


Subtract eq(3) from eq(4). You will get


10 = -R + 10 - (-15)

10 = -R + 25

10 - 25 = -R  ====>  R = 15.


Answer.  R is 15 years old.  N is (from eq(4) )   N = 2R + 10-5 = 2*15+10-5 = 35 years old.

Solved.