Kathy and Warren collect beads and pencils. Warren has 55 less beads than pencils. Warren has 3 times the number of beads Kathy has, and Kathy has 40% more pencils than Warren. After Kathy gives Warren all of her beads and Warren gives Kathy 60% of his pencils, Warren has 6 less pencils than beads. Find the number of pencils Kathy has at first.

Kathy		Warren
Pencils	Beads	Pencils	Beads
4.2 u + 77	1 u	3 u + 55	3 u
+ 1.8 u + 33	- 1 u	- 1.8 u - 33	+ 1 u
6 u + 110	0	1.2 u + 22	4 u

100%+ 40% = 140% 

140% x 3 u
= ¹⁴⁰₁₀₀ x 3 u
= 4.2 u

140% x 55
= ¹⁴⁰₁₀₀ x 55
= 77 

60% x 3 u
= ⁶⁰₁₀₀ x 3 u
= 1.8 u  

60% x 55 
= ⁶⁰₁₀₀ x 55
= 33 

If another 6 pencils are given to Warren, he will have equal number of pencils and beads in the end.
4 u = 1.2 u + 22 + 6
4 u - 1.2 u = 28
2.8 u = 28

1 u = 28 ÷ 2.8 = 10

Number of pencils that Kathy has at first
= 4.2 u + 77
= 4.2 x 10 + 77
= 42 + 77
= 119
 
Answer(s): 119