Sarah and Japheth collect stickers and buttons. Japheth has 30 less stickers than buttons. Japheth has 2 times the number of stickers Sarah has, and Sarah has 30% more buttons than Japheth. After Sarah gives Japheth all of her stickers and Japheth gives Sarah 60% of his buttons, Japheth has 21 less buttons than stickers. Find the number of buttons Sarah has at first.

Sarah		Japheth
Buttons	Stickers	Buttons	Stickers
2.6 u + 39	1 u	2 u + 30	2 u
+ 1.2 u + 18	- 1 u	- 1.2 u - 18	+ 1 u
3.8 u + 57	0	0.8 u + 12	3 u

100%+ 30% = 130% 

130% x 2 u
= ¹³⁰₁₀₀ x 2 u
= 2.6 u

130% x 30
= ¹³⁰₁₀₀ x 30
= 39 

60% x 2 u
= ⁶⁰₁₀₀ x 2 u
= 1.2 u  

60% x 30 
= ⁶⁰₁₀₀ x 30
= 18 

If another 21 buttons are given to Japheth, he will have equal number of buttons and stickers in the end.
3 u = 0.8 u + 12 + 21
3 u - 0.8 u = 33
2.2 u = 33

1 u = 33 ÷ 2.2 = 15

Number of buttons that Sarah has at first
= 2.6 u + 39
= 2.6 x 15 + 39
= 39 + 39
= 78
 
Answer(s): 78