Elyse and Owen collect pencils and buttons. Owen has 90 less pencils than buttons. Owen has 2 times the number of pencils Elyse has, and Elyse has 40% more buttons than Owen. After Elyse gives Owen all of her pencils and Owen gives Elyse 70% of his buttons, Owen has 21 less buttons than pencils. Find the number of buttons Elyse has at first.

Elyse		Owen
Buttons	Pencils	Buttons	Pencils
2.8 u + 126	1 u	2 u + 90	2 u
+ 1.4 u + 63	- 1 u	- 1.4 u - 63	+ 1 u
4.2 u + 189	0	0.6 u + 27	3 u

100%+ 40% = 140% 

140% x 2 u
= ¹⁴⁰₁₀₀ x 2 u
= 2.8 u

140% x 90
= ¹⁴⁰₁₀₀ x 90
= 126 

70% x 2 u
= ⁷⁰₁₀₀ x 2 u
= 1.4 u  

70% x 90 
= ⁷⁰₁₀₀ x 90
= 63 

If another 21 buttons are given to Owen, he will have equal number of buttons and pencils in the end.
3 u = 0.6 u + 27 + 21
3 u - 0.6 u = 48
2.4 u = 48

1 u = 48 ÷ 2.4 = 20

Number of buttons that Elyse has at first
= 2.8 u + 126
= 2.8 x 20 + 126
= 56 + 126
= 182
 
Answer(s): 182