Vanessa and Michael collect stickers and marbles. Michael has 100 more marbles than stickers. Michael has 5 times the number of stickers Vanessa has, and Vanessa has 30% more marbles than Michael. After Vanessa gives Michael all of her stickers and Michael gives Vanessa 70% of his marbles, Michael has 33 more stickers than marbles. Find the number of marbles Vanessa has at first.

Vanessa		Michael
Marbles	Stickers	Marbles	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 33 marbles are given to Michael, he will have equal number of marbles and stickers in the end.
6 u = 1.5 u + 30 + 33
6 u - 1.5 u = 63
4.5 u = 63

1 u = 63 ÷ 4.5 = 14

Number of marbles that Vanessa has at first
= 6.5 u + 130
= 6.5 x 14 + 130
= 91 + 130
= 221
 
Answer(s): 221