Dave has $d$ pieces of candy and Ramon has $r$ pieces. Dave gives Ramon $\frac {1}{3}$ of his candy. They then each have 20 pieces of candy. What is the value

We have

[d - (1/3)d ]   = 20       and

[r + (1/3)d]  = 20

Add the equations and we get that

d - r =   40      →  d =  40 + r      substituting this into the second equation, we have

r + (1/3)(40 - r)  = 20

(2/3)r + 40/3  = 20       multiply through by 3

2r + 40   = 60        divide through by 2

r + 20 = 30         r = 10         and d = 40 - 10 = 30

So....Ramon started with 10 pieces of candy and Dave started with 30