Problem 170 Solution

90% of this problem is working through the wording into the form of an equation. Let's let i be my age and j be the age of John. The first piece of information tells us...

i = 2*((i+j)/2 + (j-i)) + (j-i)
= 2*(3j-i)/2 + (j-i)
= 4j - 2i
= (4/3)*j

The second piece of information tells us...

j = (j+10)/2 + (i-j)
= i - j/2 + 5 = (2i+10)/3

Combining the two equations we get...

i = (4/3)*(2i+10)/3
= (4/9)*(2i+10)
= (8/9)*i + 40/9
= 40

So I am 40 (and John is 30).

Michael Shackleford, A.S.A.