Units and Parts (Unchanged Amount and From Equality)

First
Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates became 1 : 7. The ratio of Ken’s sweets to chocolates became 1 : 4. How many sweets did Ken buy?

(After)
(Jim)
Sweets : Chocolates
= 1u : 7u

(Ken)
Sweets : Chocolates
= 1p : 4p

Reverse the Changes

(Before)
(Sweets)
Jim Sweets = Ken Sweets
1u + 12 sweets eaten = 1p
7u + 84 = 7p

(Chocolates)
Jim Chocolates = Ken Chocolates
7u = 4p + 18 chocolates eaten
7u - 18 = 4p

84 -(-18) = 7p - 4p
3p = 102

Ken Sweets (Before) = 1p = 34