Tiffany and Ben collect coins and beads. Ben has 52 less coins than beads. Ben has 2 times the number of coins Tiffany has, and Tiffany has 25% more beads than Ben. After Tiffany gives Ben all of her coins and Ben gives Tiffany 75% of his beads, Ben has 32 more coins than beads. Find the number of beads Tiffany has at first.

Tiffany		Ben
Beads	Coins	Beads	Coins
2.5 u + 65	1 u	2 u + 52	2 u
+ 1.5 u + 39	- 1 u	- 1.5 u - 39	+ 1 u
4 u + 104	0	0.5 u + 13	3 u

100%+ 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 52
= ¹²⁵₁₀₀ x 52
= 65 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 52 
= ⁷⁵₁₀₀ x 52
= 39 

If another 32 beads are given to Ben, he will have equal number of beads and coins in the end.
3 u = 0.5 u + 13 + 32
3 u - 0.5 u = 45
2.5 u = 45

1 u = 45 ÷ 2.5 = 18

Number of beads that Tiffany has at first
= 2.5 u + 65
= 2.5 x 18 + 65
= 45 + 65
= 110
 
Answer(s): 110