Erika and Japheth collect coins and cards. Japheth has 45 more cards than coins. Japheth has 3 times the number of coins Erika has, and Erika has 40% more cards than Japheth. After Erika gives Japheth all of her coins and Japheth gives Erika 60% of his cards, Japheth has 10 more coins than cards. Find the number of cards Erika has at first.

Erika		Japheth
Cards	Coins	Cards	Coins
4.2 u + 63	1 u	3 u + 45	3 u
+ 1.8 u + 27	- 1 u	- 1.8 u - 27	+ 1 u
6 u + 90	0	1.2 u + 18	4 u

100% + 40% = 140% 

140% x 3 u
= ¹⁴⁰₁₀₀ x 3 u
= 4.2 u

140% x 45
= ¹⁴⁰₁₀₀ x 45
= 63 

60% x 3 u
= ⁶⁰₁₀₀ x 3 u
= 1.8 u  

60% x 45 
= ⁶⁰₁₀₀ x 45
= 27 

If another 10 cards are given to Japheth, he will have equal number of cards and coins in the end.
4 u = 1.2 u + 18 + 10
4 u - 1.2 u = 28
2.8 u = 28

1 u = 28 ÷ 2.8 = 10

Number of cards that Erika has at first
= 4.2 u + 63
= 4.2 x 10 + 63
= 42 + 63
= 105
 
Answer(s): 105