Ken and John had 65 marbles in total. Ken had 27 marbles less than John at first. After Ken and John played a game with Raeann, Ken had ¹₁₀ as many marbles as John. If Ken lost as many marbles as John to Raeann, find the number of marbles that John lost to Raeann.

	Ken	John	Difference
Before	1 u	1 u + 27	27
Change	- ?	- ?
After	1 p	10 p	9 p

Total number of marbles at first
= 1 u + 1 u + 27 
= 2 u + 27

2 u + 27 = 65
2 u = 65 - 27
2 u = 38

1 u = 38 ÷ 2 = 19

Since Ken lost the same number of marbles as John, the difference in the number of marbles between Ken and John at first and in the end remains the same.

Difference in the number of marbles in the end
= 10 p - 1 p
= 9 p

9 p = 27

1 p = 27 ÷ 9 = 3

Number of marbles that Ken lost to Raeann
= 1 u - 1 p
= 19 - 1 x 3
= 19 - 3
= 16

Since John lost the same number of marbles as Ken, the number of marbles that each lost to Raeann is the same.

Number of marbles that John lost = 16

Answer(s): 16