Archie and Justin had 101 marbles in total. Justin had 35 marbles more than Archie at first. After Archie and Justin played a game with Jane, Archie had ⁴₉ as many marbles as Justin. If Archie lost as many marbles as Justin to Jane, find the number of marbles that Archie lost to Jane.

	Archie	Justin	Difference
Before	1 u	1 u + 35	35
Change	- ?	- ?
After	4 p	9 p	5 p

Total number of marbles at first
= 1 u + 1 u + 35 
= 2 u + 35

2 u + 35 = 101
2 u = 101 - 35
2 u = 66

1 u = 66 ÷ 2 = 33

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

Difference in the number of marbles in the end
= 9 p - 4 p
= 5 p

5 p = 35

1 p = 35 ÷ 5 = 7

Number of marbles that Archie lost to Jane
= 1 u - 4 p
= 33 - 4 x 7
= 33 - 28
= 5

Answer(s): 5