Emily and Andy collect pens and beads. Andy has 80 less pens than beads. Andy has 2 times the number of pens Emily has, and Emily has 30% more beads than Andy. After Emily gives Andy all of her pens and Andy gives Emily 75% of his beads, Andy has 30 less beads than pens. Find the number of beads Emily has at first.

Emily		Andy
Beads	Pens	Beads	Pens
2.6 u + 104	1 u	2 u + 80	2 u
+ 1.5 u + 60	- 1 u	- 1.5 u - 60	+ 1 u
4.1 u + 164	0	0.5 u + 20	3 u

100%+ 30% = 130% 

130% x 2 u
= ¹³⁰₁₀₀ x 2 u
= 2.6 u

130% x 80
= ¹³⁰₁₀₀ x 80
= 104 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 80 
= ⁷⁵₁₀₀ x 80
= 60 

If another 30 beads are given to Andy, he will have equal number of beads and pens in the end.
3 u = 0.5 u + 20 + 30
3 u - 0.5 u = 50
2.5 u = 50

1 u = 50 ÷ 2.5 = 20

Number of beads that Emily has at first
= 2.6 u + 104
= 2.6 x 20 + 104
= 52 + 104
= 156
 
Answer(s): 156