SOLUTION: If the digits of Fathers present age are reversed then get the age of his son.If 1 year ago his age was twice as that of his son.Find his present age

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: If the digits of Fathers present age are reversed then get the age of his son.If 1 year ago his age was twice as that of his son.Find his present age      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 438274: If the digits of Fathers present age are reversed then get the age of his son.If 1 year ago his
age was twice as that of his son.Find his present age
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 10s digit of Father's age = a
Let the units digit of Father's age = b
given:
Father's age = 10a+%2B+b+
Age of Son = +10b+%2B+a+
+10a+%2B+b+-+1+=+2%2A%28+10b+%2B+a+-+1%29+
+10a+%2B+b+-+1+=+20b+%2B+2a+-+2+
+8a+=+19b+-+1+
This is 1 equation and 2 unknowns, so it's
not solvable directly.
I see that +a+%3E+b+. I also see that the left
side will always be even, so b must be
odd for that to be.
So, b can be 3,5,7
(b can't be 9, since +a%3Eb+
a can be even or odd
---------------------
+b+=+7+
+19b+-+1+=+132+
8a does not divide 132 for any a
------------------------
+b+=+5
+19b+-+1+=+94+
8a does not divide 94 for any a
------------------------
+b+=+3+
+19b+-+1+=+56+
+8a+=+56+
+a+=+7
---------
The father is 73 and the son is 37
check:
+10a+%2B+b+-+1+=+2%2A%28+10b+%2B+a+-+1%29+
+10%2A7+%2B+3+-+1+=+2%2A%28+10%2A3+%2B+7+-+1%29+
+70+%2B+2+=+2%2A%28+30+%2B+6+%29+
+72+=+72+
OK