Sarah and Jack collect buttons and pencils. Jack has 100 less buttons than pencils. Jack has 4 times the number of buttons Sarah has, and Sarah has 30% more pencils than Jack. After Sarah gives Jack all of her buttons and Jack gives Sarah 75% of his pencils, Jack has 15 more buttons than pencils. Find the number of pencils Sarah has at first.

Sarah		Jack
Pencils	Buttons	Pencils	Buttons
5.2 u + 130	1 u	4 u + 100	4 u
+ 3 u + 75	- 1 u	- 3 u - 75	+ 1 u
8.2 u + 205	0	1 u + 25	5 u

100%+ 30% = 130% 

130% x 4 u
= ¹³⁰₁₀₀ x 4 u
= 5.2 u

130% x 100
= ¹³⁰₁₀₀ x 100
= 130 

75% x 4 u
= ⁷⁵₁₀₀ x 4 u
= 3 u  

75% x 100 
= ⁷⁵₁₀₀ x 100
= 75 

If another 15 pencils are given to Jack, he will have equal number of pencils and buttons in the end.
5 u = 1 u + 25 + 15
5 u - 1 u = 40
4 u = 40

1 u = 40 ÷ 4 = 10

Number of pencils that Sarah has at first
= 5.2 u + 130
= 5.2 x 10 + 130
= 52 + 130
= 182
 
Answer(s): 182