Question 1122872
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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.


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