Fanny and Luis collect stickers and pencils. Luis has 100 less stickers than pencils. Luis has 5 times the number of stickers Fanny has, and Fanny has 30% more pencils than Luis. After Fanny gives Luis all of her stickers and Luis gives Fanny 70% of his pencils, Luis has 24 less pencils than stickers. Find the number of pencils Fanny has at first.

Fanny		Luis
Pencils	Stickers	Pencils	Stickers
6.5 u + 130	1 u	5 u + 100	5 u
+ 3.5 u + 70	- 1 u	- 3.5 u - 70	+ 1 u
10 u + 200	0	1.5 u + 30	6 u

100%+ 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 100
= ¹³⁰₁₀₀ x 100
= 130 

70% x 5 u
= ⁷⁰₁₀₀ x 5 u
= 3.5 u  

70% x 100 
= ⁷⁰₁₀₀ x 100
= 70 

If another 24 pencils are given to Luis, he will have equal number of pencils and stickers in the end.
6 u = 1.5 u + 30 + 24
6 u - 1.5 u = 54
4.5 u = 54

1 u = 54 ÷ 4.5 = 12

Number of pencils that Fanny has at first
= 6.5 u + 130
= 6.5 x 12 + 130
= 78 + 130
= 208
 
Answer(s): 208