Kimberly and Peter collect pens and buttons. Peter has 40 less pens than buttons. Peter has 3 times the number of pens Kimberly has, and Kimberly has 40% more buttons than Peter. After Kimberly gives Peter all of her pens and Peter gives Kimberly 70% of his buttons, Peter has 19 more pens than buttons. Find the number of buttons Kimberly has at first.

Kimberly		Peter
Buttons	Pens	Buttons	Pens
4.2 u + 56	1 u	3 u + 40	3 u
+ 2.1 u + 28	- 1 u	- 2.1 u - 28	+ 1 u
6.3 u + 84	0	0.9 u + 12	4 u

100%+ 40% = 140% 

140% x 3 u
= ¹⁴⁰₁₀₀ x 3 u
= 4.2 u

140% x 40
= ¹⁴⁰₁₀₀ x 40
= 56 

70% x 3 u
= ⁷⁰₁₀₀ x 3 u
= 2.1 u  

70% x 40 
= ⁷⁰₁₀₀ x 40
= 28 

If another 19 buttons are given to Peter, he will have equal number of buttons and pens in the end.
4 u = 0.9 u + 12 + 19
4 u - 0.9 u = 31
3.1 u = 31

1 u = 31 ÷ 3.1 = 10

Number of buttons that Kimberly has at first
= 4.2 u + 56
= 4.2 x 10 + 56
= 42 + 56
= 98
 
Answer(s): 98