Dana and Oscar collect beads and buttons. Oscar has 70 more buttons than beads. Oscar has 2 times the number of beads Dana has, and Dana has 30% more buttons than Oscar. After Dana gives Oscar all of her beads and Oscar gives Dana 70% of his buttons, Oscar has 15 more beads than buttons. Find the number of buttons Dana has at first.

Dana		Oscar
Buttons	Beads	Buttons	Beads
2.6 u + 91	1 u	2 u + 70	2 u
+ 1.4 u + 49	- 1 u	- 1.4 u - 49	+ 1 u
4 u + 140	0	0.6 u + 21	3 u

100% + 30% = 130% 

130% x 2 u
= ¹³⁰₁₀₀ x 2 u
= 2.6 u

130% x 70
= ¹³⁰₁₀₀ x 70
= 91 

70% x 2 u
= ⁷⁰₁₀₀ x 2 u
= 1.4 u  

70% x 70 
= ⁷⁰₁₀₀ x 70
= 49 

If another 15 buttons are given to Oscar, he will have equal number of buttons and beads in the end.
3 u = 0.6 u + 21 + 15
3 u - 0.6 u = 36
2.4 u = 36

1 u = 36 ÷ 2.4 = 15

Number of buttons that Dana has at first
= 2.6 u + 91
= 2.6 x 15 + 91
= 39 + 91
= 130
 
Answer(s): 130