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5 years ago kate was 5 times as old as her son 5 years hence her age will be 8 less than three times the corresponding age of her son find their ages?
Let X = KATE's AGE
LET Y = SON's age
5 years ago Kate was x-5 years old and her son Y-5 years old
Kate was then five times oldertah son so
x-5 = 5(y-5)in five years hence Kate will be X+5 years old and son Y + 5
Kate will be 8 less than 3 times son then so
x + 5 = 3 (Y+5) -8
so you have two equations in twounknowns to solve
x-5 = 5y - 25
x + 5 = 3y+15-8
x - 5y = -20
x-3y = 2
subtract and find
-2y = -22
Y = 11 years old son age
from either equation
x-5(11) = -20
X -55 = -20
X = 35 KATE's age
X =
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