Victoria and Sean collect buttons and marbles. Sean has 40 more marbles than buttons. Sean has 5 times the number of buttons Victoria has, and Victoria has 30% more marbles than Sean. After Victoria gives Sean all of her buttons and Sean gives Victoria 70% of his marbles, Sean has 42 more buttons than marbles. Find the number of marbles Victoria has at first.

Victoria		Sean
Marbles	Buttons	Marbles	Buttons
6.5 u + 52	1 u	5 u + 40	5 u
+ 3.5 u + 28	- 1 u	- 3.5 u - 28	+ 1 u
10 u + 80	0	1.5 u + 12	6 u

100% + 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 40
= ¹³⁰₁₀₀ x 40
= 52 

70% x 5 u
= ⁷⁰₁₀₀ x 5 u
= 3.5 u  

70% x 40 
= ⁷⁰₁₀₀ x 40
= 28 

If another 42 marbles are given to Sean, he will have equal number of marbles and buttons in the end.
6 u = 1.5 u + 12 + 42
6 u - 1.5 u = 54
4.5 u = 54

1 u = 54 ÷ 4.5 = 12

Number of marbles that Victoria has at first
= 6.5 u + 52
= 6.5 x 12 + 52
= 78 + 52
= 130
 
Answer(s): 130