Barbara and Ethan collect stickers and pencils. Ethan has 60 less stickers than pencils. Ethan has 3 times the number of stickers Barbara has, and Barbara has 40% more pencils than Ethan. After Barbara gives Ethan all of her stickers and Ethan gives Barbara 70% of his pencils, Ethan has 13 less pencils than stickers. Find the number of pencils Barbara has at first.

Barbara		Ethan
Pencils	Stickers	Pencils	Stickers
4.2 u + 84	1 u	3 u + 60	3 u
+ 2.1 u + 42	- 1 u	- 2.1 u - 42	+ 1 u
6.3 u + 126	0	0.9 u + 18	4 u

100%+ 40% = 140% 

140% x 3 u
= ¹⁴⁰₁₀₀ x 3 u
= 4.2 u

140% x 60
= ¹⁴⁰₁₀₀ x 60
= 84 

70% x 3 u
= ⁷⁰₁₀₀ x 3 u
= 2.1 u  

70% x 60 
= ⁷⁰₁₀₀ x 60
= 42 

If another 13 pencils are given to Ethan, he will have equal number of pencils and stickers in the end.
4 u = 0.9 u + 18 + 13
4 u - 0.9 u = 31
3.1 u = 31

1 u = 31 ÷ 3.1 = 10

Number of pencils that Barbara has at first
= 4.2 u + 84
= 4.2 x 10 + 84
= 42 + 84
= 126
 
Answer(s): 126