SOLUTION: A grandfather is 50 years older than his grandson. Five years ago he was six times as old as his grandson was then. How old is the grandfather now?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: A grandfather is 50 years older than his grandson. Five years ago he was six times as old as his grandson was then. How old is the grandfather now?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 600588: A grandfather is 50 years older than his grandson. Five years ago he was six times as old as his grandson was then. How old is the grandfather now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Grandson's age now
Let +b+ = Grandfather's age now
given:
(1) +b+=+a+%2B+50+
(2) +b+-+5+=+6%2A%28+a+-+5+%29+
----------------------
Substitute (1) into (2)
(2) +a+%2B+50+-+5+=+6a+-+30+
(2) +6a+-+a+=+50+-+5+%2B+30+
(2) +5a+=+75+
(2) +a+=+15+
and, since,
(1) +b+=+a+%2B+50+
(1) +b+=+15+%2B+50+
(1) +b+=+65+
The Grandfather is 65
check:
(2) +65+-+5+=+6%2A%28+a+-+5+%29+
(2) +60+=+6%2A%28+15+-+5+%29+
(2) +60+=+60+
OK