Xuan and Jeremy collect pens and beads. Jeremy has 100 less pens than beads. Jeremy has 5 times the number of pens Xuan has, and Xuan has 25% more beads than Jeremy. After Xuan gives Jeremy all of her pens and Jeremy gives Xuan 75% of his beads, Jeremy has 51 more pens than beads. Find the number of beads Xuan has at first.

Xuan		Jeremy
Beads	Pens	Beads	Pens
6.25 u + 125	1 u	5 u + 100	5 u
+ 3.75 u + 75	- 1 u	- 3.75 u - 75	+ 1 u
10 u + 200	0	1.25 u + 25	6 u

100%+ 25% = 125% 

125% x 5 u
= ¹²⁵₁₀₀ x 5 u
= 6.25 u

125% x 100
= ¹²⁵₁₀₀ x 100
= 125 

75% x 5 u
= ⁷⁵₁₀₀ x 5 u
= 3.75 u  

75% x 100 
= ⁷⁵₁₀₀ x 100
= 75 

If another 51 beads are given to Jeremy, he will have equal number of beads and pens in the end.
6 u = 1.25 u + 25 + 51
6 u - 1.25 u = 76
4.75 u = 76

1 u = 76 ÷ 4.75 = 16

Number of beads that Xuan has at first
= 6.25 u + 125
= 6.25 x 16 + 125
= 100 + 125
= 225
 
Answer(s): 225