Gem and Ivan collect stickers and marbles. Ivan has 96 more marbles than stickers. Ivan has 3 times the number of stickers Gem has, and Gem has 25% more marbles than Ivan. After Gem gives Ivan all of her stickers and Ivan gives Gem 75% of his marbles, Ivan has 15 more stickers than marbles. Find the number of marbles Gem has at first.

Gem		Ivan
Marbles	Stickers	Marbles	Stickers
3.75 u + 120	1 u	3 u + 96	3 u
+ 2.25 u + 72	- 1 u	- 2.25 u - 72	+ 1 u
6 u + 192	0	0.75 u + 24	4 u

100% + 25% = 125% 

125% x 3 u
= ¹²⁵₁₀₀ x 3 u
= 3.75 u

125% x 96
= ¹²⁵₁₀₀ x 96
= 120 

75% x 3 u
= ⁷⁵₁₀₀ x 3 u
= 2.25 u  

75% x 96 
= ⁷⁵₁₀₀ x 96
= 72 

If another 15 marbles are given to Ivan, he will have equal number of marbles and stickers in the end.
4 u = 0.75 u + 24 + 15
4 u - 0.75 u = 39
3.25 u = 39

1 u = 39 ÷ 3.25 = 12

Number of marbles that Gem has at first
= 3.75 u + 120
= 3.75 x 12 + 120
= 45 + 120
= 165
 
Answer(s): 165