Age Problem 6 Solution

This is the answer to the age algebra word problem that asked, "Bob is one third the age of his father. In 12 years he will be half the age of his father. How old is each now?"


Ok Bob being 1/3 the age of his father is the same thing as saying the father is 3 times as old as him.  It makes it easier to work with.  So let Bob be x and his father be 3x. And in 12 years bob will be half as old as his father.  So we have..


x + 12 =  (3x + 12) / 2

2x + 24 = 3x + 12

x  = 12


So Bob is 12 years old and his father is 3(12) or 36 years old now.  In 12 years Bob will be 12 + 12  or 24 years old and his father will be 36 + 12 or 48 years old which means Bob will be half as old so it checks out.