Xuan and Tommy collect pens and buttons. Tommy has 100 more buttons than pens. Tommy has 4 times the number of pens Xuan has, and Xuan has 40% more buttons than Tommy. After Xuan gives Tommy all of her pens and Tommy gives Xuan 70% of his buttons, Tommy has 46 more pens than buttons. Find the number of buttons Xuan has at first.

Xuan		Tommy
Buttons	Pens	Buttons	Pens
5.6 u + 140	1 u	4 u + 100	4 u
+ 2.8 u + 70	- 1 u	- 2.8 u - 70	+ 1 u
8.4 u + 210	0	1.2 u + 30	5 u

100% + 40% = 140% 

140% x 4 u
= ¹⁴⁰₁₀₀ x 4 u
= 5.6 u

140% x 100
= ¹⁴⁰₁₀₀ x 100
= 140 

70% x 4 u
= ⁷⁰₁₀₀ x 4 u
= 2.8 u  

70% x 100 
= ⁷⁰₁₀₀ x 100
= 70 

If another 46 buttons are given to Tommy, he will have equal number of buttons and pens in the end.
5 u = 1.2 u + 30 + 46
5 u - 1.2 u = 76
3.8 u = 76

1 u = 76 ÷ 3.8 = 20

Number of buttons that Xuan has at first
= 5.6 u + 140
= 5.6 x 20 + 140
= 112 + 140
= 252
 
Answer(s): 252