Opal and Tommy collect beads and buttons. Tommy has 55 less beads than buttons. Tommy has 4 times the number of beads Opal has, and Opal has 20% more buttons than Tommy. After Opal gives Tommy all of her beads and Tommy gives Opal 60% of his buttons, Tommy has 29 more beads than buttons. Find the number of buttons Opal has at first.

Opal		Tommy
Buttons	Beads	Buttons	Beads
4.8 u + 66	1 u	4 u + 55	4 u
+ 2.4 u + 33	- 1 u	- 2.4 u - 33	+ 1 u
7.2 u + 99	0	1.6 u + 22	5 u

100%+ 20% = 120% 

120% x 4 u
= ¹²⁰₁₀₀ x 4 u
= 4.8 u

120% x 55
= ¹²⁰₁₀₀ x 55
= 66 

60% x 4 u
= ⁶⁰₁₀₀ x 4 u
= 2.4 u  

60% x 55 
= ⁶⁰₁₀₀ x 55
= 33 

If another 29 buttons are given to Tommy, he will have equal number of buttons and beads in the end.
5 u = 1.6 u + 22 + 29
5 u - 1.6 u = 51
3.4 u = 51

1 u = 51 ÷ 3.4 = 15

Number of buttons that Opal has at first
= 4.8 u + 66
= 4.8 x 15 + 66
= 72 + 66
= 138
 
Answer(s): 138