Betty and Bobby collect stickers and buttons. Bobby has 40 less stickers than buttons. Bobby has 2 times the number of stickers Betty has, and Betty has 20% more buttons than Bobby. After Betty gives Bobby all of her stickers and Bobby gives Betty 75% of his buttons, Bobby has 40 less buttons than stickers. Find the number of buttons Betty has at first.

Betty		Bobby
Buttons	Stickers	Buttons	Stickers
2.4 u + 48	1 u	2 u + 40	2 u
+ 1.5 u + 30	- 1 u	- 1.5 u - 30	+ 1 u
3.9 u + 78	0	0.5 u + 10	3 u

100%+ 20% = 120% 

120% x 2 u
= ¹²⁰₁₀₀ x 2 u
= 2.4 u

120% x 40
= ¹²⁰₁₀₀ x 40
= 48 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 40 
= ⁷⁵₁₀₀ x 40
= 30 

If another 40 buttons are given to Bobby, he will have equal number of buttons and stickers in the end.
3 u = 0.5 u + 10 + 40
3 u - 0.5 u = 50
2.5 u = 50

1 u = 50 ÷ 2.5 = 20

Number of buttons that Betty has at first
= 2.4 u + 48
= 2.4 x 20 + 48
= 48 + 48
= 96
 
Answer(s): 96