Sam and Japheth had 46 marbles in total. Japheth had 10 marbles more than Sam at first. After Sam and Japheth played a game with Nicole, Sam had ¹₆ as many marbles as Japheth. If Sam lost as many marbles as Japheth to Nicole, find the number of marbles that Sam lost to Nicole.

	Sam	Japheth	Difference
Before	1 u	1 u + 10	10
Change	- ?	- ?
After	1 p	6 p	5 p

Total number of marbles at first
= 1 u + 1 u + 10 
= 2 u + 10

2 u + 10 = 46
2 u = 46 - 10
2 u = 36

1 u = 36 ÷ 2 = 18

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

Difference in the number of marbles in the end
= 6 p - 1 p
= 5 p

5 p = 10

1 p = 10 ÷ 5 = 2

Number of marbles that Sam lost to Nicole
= 1 u - 1 p
= 18 - 1 x 2
= 18 - 2
= 16

Answer(s): 16