Emily and Sean collect coins and beads. Sean has 48 more beads than coins. Sean has 2 times the number of coins Emily has, and Emily has 25% more beads than Sean. After Emily gives Sean all of her coins and Sean gives Emily 75% of his beads, Sean has 28 more coins than beads. Find the number of beads Emily has at first.

Emily		Sean
Beads	Coins	Beads	Coins
2.5 u + 60	1 u	2 u + 48	2 u
+ 1.5 u + 36	- 1 u	- 1.5 u - 36	+ 1 u
4 u + 96	0	0.5 u + 12	3 u

100% + 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 48
= ¹²⁵₁₀₀ x 48
= 60 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 48 
= ⁷⁵₁₀₀ x 48
= 36 

If another 28 beads are given to Sean, he will have equal number of beads and coins in the end.
3 u = 0.5 u + 12 + 28
3 u - 0.5 u = 40
2.5 u = 40

1 u = 40 ÷ 2.5 = 16

Number of beads that Emily has at first
= 2.5 u + 60
= 2.5 x 16 + 60
= 40 + 60
= 100
 
Answer(s): 100