Raeann and Peter collect pens and pencils. Peter has 55 more pencils than pens. Peter has 2 times the number of pens Raeann has, and Raeann has 20% more pencils than Peter. After Raeann gives Peter all of her pens and Peter gives Raeann 60% of his pencils, Peter has 11 more pens than pencils. Find the number of pencils Raeann has at first.

Raeann		Peter
Pencils	Pens	Pencils	Pens
2.4 u + 66	1 u	2 u + 55	2 u
+ 1.2 u + 33	- 1 u	- 1.2 u - 33	+ 1 u
3.6 u + 99	0	0.8 u + 22	3 u

100% + 20% = 120% 

120% x 2 u
= ¹²⁰₁₀₀ x 2 u
= 2.4 u

120% x 55
= ¹²⁰₁₀₀ x 55
= 66 

60% x 2 u
= ⁶⁰₁₀₀ x 2 u
= 1.2 u  

60% x 55 
= ⁶⁰₁₀₀ x 55
= 33 

If another 11 pencils are given to Peter, he will have equal number of pencils and pens in the end.
3 u = 0.8 u + 22 + 11
3 u - 0.8 u = 33
2.2 u = 33

1 u = 33 ÷ 2.2 = 15

Number of pencils that Raeann has at first
= 2.4 u + 66
= 2.4 x 15 + 66
= 36 + 66
= 102
 
Answer(s): 102