Tim and Bryan had 105 marbles in total. Bryan had 35 marbles more than Tim at first. After Tim and Bryan played a game with Gillian, Tim had ³₁₀ as many marbles as Bryan. If Tim lost as many marbles as Bryan to Gillian, find the number of marbles that Tim lost to Gillian.

	Tim	Bryan	Difference
Before	1 u	1 u + 35	35
Change	- ?	- ?
After	3 p	10 p	7 p

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

2 u + 35 = 105
2 u = 105 - 35
2 u = 70

1 u = 70 ÷ 2 = 35

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

Difference in the number of marbles in the end
= 10 p - 3 p
= 7 p

7 p = 35

1 p = 35 ÷ 7 = 5

Number of marbles that Tim lost to Gillian
= 1 u - 3 p
= 35 - 3 x 5
= 35 - 15
= 20

Answer(s): 20