Ivory and Fred collect coins and cards. Fred has 36 more cards than coins. Fred has 2 times the number of coins Ivory has, and Ivory has 25% more cards than Fred. After Ivory gives Fred all of her coins and Fred gives Ivory 75% of his cards, Fred has 36 more coins than cards. Find the number of cards Ivory has at first.

Ivory		Fred
Cards	Coins	Cards	Coins
2.5 u + 45	1 u	2 u + 36	2 u
+ 1.5 u + 27	- 1 u	- 1.5 u - 27	+ 1 u
4 u + 72	0	0.5 u + 9	3 u

100% + 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 36
= ¹²⁵₁₀₀ x 36
= 45 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 36 
= ⁷⁵₁₀₀ x 36
= 27 

If another 36 cards are given to Fred, he will have equal number of cards and coins in the end.
3 u = 0.5 u + 9 + 36
3 u - 0.5 u = 45
2.5 u = 45

1 u = 45 ÷ 2.5 = 18

Number of cards that Ivory has at first
= 2.5 u + 45
= 2.5 x 18 + 45
= 45 + 45
= 90
 
Answer(s): 90