Opal and Nick collect buttons and pencils. Nick has 100 less buttons than pencils. Nick has 4 times the number of buttons Opal has, and Opal has 20% more pencils than Nick. After Opal gives Nick all of her buttons and Nick gives Opal 70% of his pencils, Nick has 27 less pencils than buttons. Find the number of pencils Opal has at first.

Opal		Nick
Pencils	Buttons	Pencils	Buttons
4.8 u + 120	1 u	4 u + 100	4 u
+ 2.8 u + 70	- 1 u	- 2.8 u - 70	+ 1 u
7.6 u + 190	0	1.2 u + 30	5 u

100%+ 20% = 120% 

120% x 4 u
= ¹²⁰₁₀₀ x 4 u
= 4.8 u

120% x 100
= ¹²⁰₁₀₀ x 100
= 120 

70% x 4 u
= ⁷⁰₁₀₀ x 4 u
= 2.8 u  

70% x 100 
= ⁷⁰₁₀₀ x 100
= 70 

If another 27 pencils are given to Nick, he will have equal number of pencils and buttons in the end.
5 u = 1.2 u + 30 + 27
5 u - 1.2 u = 57
3.8 u = 57

1 u = 57 ÷ 3.8 = 15

Number of pencils that Opal has at first
= 4.8 u + 120
= 4.8 x 15 + 120
= 72 + 120
= 192
 
Answer(s): 192