Gabby and Vincent collect erasers and cards. Vincent has 40 more cards than erasers. Vincent has 2 times the number of erasers Gabby has, and Gabby has 25% more cards than Vincent. After Gabby gives Vincent all of her erasers and Vincent gives Gabby 75% of his cards, Vincent has 10 more erasers than cards. Find the number of cards Gabby has at first.

Gabby		Vincent
Cards	Erasers	Cards	Erasers
2.5 u + 50	1 u	2 u + 40	2 u
+ 1.5 u + 30	- 1 u	- 1.5 u - 30	+ 1 u
4 u + 80	0	0.5 u + 10	3 u

100% + 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 40
= ¹²⁵₁₀₀ x 40
= 50 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 40 
= ⁷⁵₁₀₀ x 40
= 30 

If another 10 cards are given to Vincent, he will have equal number of cards and erasers in the end.
3 u = 0.5 u + 10 + 10
3 u - 0.5 u = 20
2.5 u = 20

1 u = 20 ÷ 2.5 = 8

Number of cards that Gabby has at first
= 2.5 u + 50
= 2.5 x 8 + 50
= 20 + 50
= 70
 
Answer(s): 70