Zara and Cole collect buttons and pencils. Cole has 100 less buttons than pencils. Cole has 4 times the number of buttons Zara has, and Zara has 30% more pencils than Cole. After Zara gives Cole all of her buttons and Cole gives Zara 60% of his pencils, Cole has 28 more buttons than pencils. Find the number of pencils Zara has at first.

Zara		Cole
Pencils	Buttons	Pencils	Buttons
5.2 u + 130	1 u	4 u + 100	4 u
+ 2.4 u + 60	- 1 u	- 2.4 u - 60	+ 1 u
7.6 u + 190	0	1.6 u + 40	5 u

100%+ 30% = 130% 

130% x 4 u
= ¹³⁰₁₀₀ x 4 u
= 5.2 u

130% x 100
= ¹³⁰₁₀₀ x 100
= 130 

60% x 4 u
= ⁶⁰₁₀₀ x 4 u
= 2.4 u  

60% x 100 
= ⁶⁰₁₀₀ x 100
= 60 

If another 28 pencils are given to Cole, he will have equal number of pencils and buttons in the end.
5 u = 1.6 u + 40 + 28
5 u - 1.6 u = 68
3.4 u = 68

1 u = 68 ÷ 3.4 = 20

Number of pencils that Zara has at first
= 5.2 u + 130
= 5.2 x 20 + 130
= 104 + 130
= 234
 
Answer(s): 234