Roshel and Mark collect beads and buttons. Mark has 88 more buttons than beads. Mark has 2 times the number of beads Roshel has, and Roshel has 25% more buttons than Mark. After Roshel gives Mark all of her beads and Mark gives Roshel 75% of his buttons, Mark has 18 more beads than buttons. Find the number of buttons Roshel has at first.

Roshel		Mark
Buttons	Beads	Buttons	Beads
2.5 u + 110	1 u	2 u + 88	2 u
+ 1.5 u + 66	- 1 u	- 1.5 u - 66	+ 1 u
4 u + 176	0	0.5 u + 22	3 u

100% + 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 88
= ¹²⁵₁₀₀ x 88
= 110 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 88 
= ⁷⁵₁₀₀ x 88
= 66 

If another 18 buttons are given to Mark, he will have equal number of buttons and beads in the end.
3 u = 0.5 u + 22 + 18
3 u - 0.5 u = 40
2.5 u = 40

1 u = 40 ÷ 2.5 = 16

Number of buttons that Roshel has at first
= 2.5 u + 110
= 2.5 x 16 + 110
= 40 + 110
= 150
 
Answer(s): 150