Yen and Justin collect buttons and marbles. Justin has 32 less buttons than marbles. Justin has 2 times the number of buttons Yen has, and Yen has 25% more marbles than Justin. After Yen gives Justin all of her buttons and Justin gives Yen 75% of his marbles, Justin has 37 more buttons than marbles. Find the number of marbles Yen has at first.

Yen		Justin
Marbles	Buttons	Marbles	Buttons
2.5 u + 40	1 u	2 u + 32	2 u
+ 1.5 u + 24	- 1 u	- 1.5 u - 24	+ 1 u
4 u + 64	0	0.5 u + 8	3 u

100%+ 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 32
= ¹²⁵₁₀₀ x 32
= 40 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 32 
= ⁷⁵₁₀₀ x 32
= 24 

If another 37 marbles are given to Justin, he will have equal number of marbles and buttons in the end.
3 u = 0.5 u + 8 + 37
3 u - 0.5 u = 45
2.5 u = 45

1 u = 45 ÷ 2.5 = 18

Number of marbles that Yen has at first
= 2.5 u + 40
= 2.5 x 18 + 40
= 45 + 40
= 85
 
Answer(s): 85