Grandfather is #15# time the age of his grandson today, in #10# years the grandson will be #3/17# the age of the grandfather. How old are the grandfather and grandson?

1 Answer
Alan P.
Apr 24, 2016

Grandfather is #65# years old.
Grandson is #5# years old.

Explanation:

Let the grandfather's age be #x#
and the grandson's age be #y#.

We are told
#color(white)("XXX")x=15y#
and
#color(white)("XXX")y+10=3/17(x+10)#

#color(white)("XXXXXX")rarr 17y+170=3x+30#

#color(white)("XXXXXXXXXXXXXX")=45y+30# (since #x=15y#)

#color(white)("XXXXXX")rarr140=28y#

#color(white)("XXXXXX")rarry=5#

#color(white)("XXX")x=15y=65#

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