Xylia and Zane collect beads and pencils. Zane has 60 less beads than pencils. Zane has 4 times the number of beads Xylia has, and Xylia has 20% more pencils than Zane. After Xylia gives Zane all of her beads and Zane gives Xylia 75% of his pencils, Zane has 5 more beads than pencils. Find the number of pencils Xylia has at first.

Xylia		Zane
Pencils	Beads	Pencils	Beads
4.8 u + 72	1 u	4 u + 60	4 u
+ 3 u + 45	- 1 u	- 3 u - 45	+ 1 u
7.8 u + 117	0	1 u + 15	5 u

100%+ 20% = 120% 

120% x 4 u
= ¹²⁰₁₀₀ x 4 u
= 4.8 u

120% x 60
= ¹²⁰₁₀₀ x 60
= 72 

75% x 4 u
= ⁷⁵₁₀₀ x 4 u
= 3 u  

75% x 60 
= ⁷⁵₁₀₀ x 60
= 45 

If another 5 pencils are given to Zane, he will have equal number of pencils and beads in the end.
5 u = 1 u + 15 + 5
5 u - 1 u = 20
4 u = 20

1 u = 20 ÷ 4 = 5

Number of pencils that Xylia has at first
= 4.8 u + 72
= 4.8 x 5 + 72
= 24 + 72
= 96
 
Answer(s): 96