Harry and Vincent had 127 marbles in total. Harry had 77 marbles less than Vincent at first. After Harry and Vincent played a game with Emily, Harry had ¹₈ as many marbles as Vincent. If Harry lost as many marbles as Vincent to Emily, find the number of marbles that Vincent lost to Emily.

	Harry	Vincent	Difference
Before	1 u	1 u + 77	77
Change	- ?	- ?
After	1 p	8 p	7 p

Total number of marbles at first
= 1 u + 1 u + 77 
= 2 u + 77

2 u + 77 = 127
2 u = 127 - 77
2 u = 50

1 u = 50 ÷ 2 = 25

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

Difference in the number of marbles in the end
= 8 p - 1 p
= 7 p

7 p = 77

1 p = 77 ÷ 7 = 11

Number of marbles that Harry lost to Emily
= 1 u - 1 p
= 25 - 1 x 11
= 25 - 11
= 14

Since Vincent lost the same number of marbles as Harry, the number of marbles that each lost to Emily is the same.

Number of marbles that Vincent lost = 14

Answer(s): 14