Elyse and Julian collect coins and cards. Julian has 60 less coins than cards. Julian has 4 times the number of coins Elyse has, and Elyse has 30% more cards than Julian. After Elyse gives Julian all of her coins and Julian gives Elyse 75% of his cards, Julian has 65 less cards than coins. Find the number of cards Elyse has at first.

Elyse		Julian
Cards	Coins	Cards	Coins
5.2 u + 78	1 u	4 u + 60	4 u
+ 3 u + 45	- 1 u	- 3 u - 45	+ 1 u
8.2 u + 123	0	1 u + 15	5 u

100%+ 30% = 130% 

130% x 4 u
= ¹³⁰₁₀₀ x 4 u
= 5.2 u

130% x 60
= ¹³⁰₁₀₀ x 60
= 78 

75% x 4 u
= ⁷⁵₁₀₀ x 4 u
= 3 u  

75% x 60 
= ⁷⁵₁₀₀ x 60
= 45 

If another 65 cards are given to Julian, he will have equal number of cards and coins in the end.
5 u = 1 u + 15 + 65
5 u - 1 u = 80
4 u = 80

1 u = 80 ÷ 4 = 20

Number of cards that Elyse has at first
= 5.2 u + 78
= 5.2 x 20 + 78
= 104 + 78
= 182
 
Answer(s): 182