Hilda and Vincent collect cards and buttons. Vincent has 52 less cards than buttons. Vincent has 3 times the number of cards Hilda has, and Hilda has 25% more buttons than Vincent. After Hilda gives Vincent all of her cards and Vincent gives Hilda 75% of his buttons, Vincent has 52 less buttons than cards. Find the number of buttons Hilda has at first.

Hilda		Vincent
Buttons	Cards	Buttons	Cards
3.75 u + 65	1 u	3 u + 52	3 u
+ 2.25 u + 39	- 1 u	- 2.25 u - 39	+ 1 u
6 u + 104	0	0.75 u + 13	4 u

100%+ 25% = 125% 

125% x 3 u
= ¹²⁵₁₀₀ x 3 u
= 3.75 u

125% x 52
= ¹²⁵₁₀₀ x 52
= 65 

75% x 3 u
= ⁷⁵₁₀₀ x 3 u
= 2.25 u  

75% x 52 
= ⁷⁵₁₀₀ x 52
= 39 

If another 52 buttons are given to Vincent, he will have equal number of buttons and cards in the end.
4 u = 0.75 u + 13 + 52
4 u - 0.75 u = 65
3.25 u = 65

1 u = 65 ÷ 3.25 = 20

Number of buttons that Hilda has at first
= 3.75 u + 65
= 3.75 x 20 + 65
= 75 + 65
= 140
 
Answer(s): 140