Pamela and Vincent collect pencils and cards. Vincent has 50 more cards than pencils. Vincent has 4 times the number of pencils Pamela has, and Pamela has 40% more cards than Vincent. After Pamela gives Vincent all of her pencils and Vincent gives Pamela 70% of his cards, Vincent has 23 more pencils than cards. Find the number of cards Pamela has at first.

Pamela		Vincent
Cards	Pencils	Cards	Pencils
5.6 u + 70	1 u	4 u + 50	4 u
+ 2.8 u + 35	- 1 u	- 2.8 u - 35	+ 1 u
8.4 u + 105	0	1.2 u + 15	5 u

100% + 40% = 140% 

140% x 4 u
= ¹⁴⁰₁₀₀ x 4 u
= 5.6 u

140% x 50
= ¹⁴⁰₁₀₀ x 50
= 70 

70% x 4 u
= ⁷⁰₁₀₀ x 4 u
= 2.8 u  

70% x 50 
= ⁷⁰₁₀₀ x 50
= 35 

If another 23 cards are given to Vincent, he will have equal number of cards and pencils in the end.
5 u = 1.2 u + 15 + 23
5 u - 1.2 u = 38
3.8 u = 38

1 u = 38 ÷ 3.8 = 10

Number of cards that Pamela has at first
= 5.6 u + 70
= 5.6 x 10 + 70
= 56 + 70
= 126
 
Answer(s): 126