Rachel and Luke collect cards and stickers. Luke has 35 more stickers than cards. Luke has 2 times the number of cards Rachel has, and Rachel has 40% more stickers than Luke. After Rachel gives Luke all of her cards and Luke gives Rachel 60% of his stickers, Luke has 19 more cards than stickers. Find the number of stickers Rachel has at first.

Rachel		Luke
Stickers	Cards	Stickers	Cards
2.8 u + 49	1 u	2 u + 35	2 u
+ 1.2 u + 21	- 1 u	- 1.2 u - 21	+ 1 u
4 u + 70	0	0.8 u + 14	3 u

100% + 40% = 140% 

140% x 2 u
= ¹⁴⁰₁₀₀ x 2 u
= 2.8 u

140% x 35
= ¹⁴⁰₁₀₀ x 35
= 49 

60% x 2 u
= ⁶⁰₁₀₀ x 2 u
= 1.2 u  

60% x 35 
= ⁶⁰₁₀₀ x 35
= 21 

If another 19 stickers are given to Luke, he will have equal number of stickers and cards in the end.
3 u = 0.8 u + 14 + 19
3 u - 0.8 u = 33
2.2 u = 33

1 u = 33 ÷ 2.2 = 15

Number of stickers that Rachel has at first
= 2.8 u + 49
= 2.8 x 15 + 49
= 42 + 49
= 91
 
Answer(s): 91