Tammy and Rael collect cards and coins. Rael has 40 more coins than cards. Rael has 2 times the number of cards Tammy has, and Tammy has 20% more coins than Rael. After Tammy gives Rael all of her cards and Rael gives Tammy 60% of his coins, Rael has 17 more cards than coins. Find the number of coins Tammy has at first.

Tammy		Rael
Coins	Cards	Coins	Cards
2.4 u + 48	1 u	2 u + 40	2 u
+ 1.2 u + 24	- 1 u	- 1.2 u - 24	+ 1 u
3.6 u + 72	0	0.8 u + 16	3 u

100% + 20% = 120% 

120% x 2 u
= ¹²⁰₁₀₀ x 2 u
= 2.4 u

120% x 40
= ¹²⁰₁₀₀ x 40
= 48 

60% x 2 u
= ⁶⁰₁₀₀ x 2 u
= 1.2 u  

60% x 40 
= ⁶⁰₁₀₀ x 40
= 24 

If another 17 coins are given to Rael, he will have equal number of coins and cards in the end.
3 u = 0.8 u + 16 + 17
3 u - 0.8 u = 33
2.2 u = 33

1 u = 33 ÷ 2.2 = 15

Number of coins that Tammy has at first
= 2.4 u + 48
= 2.4 x 15 + 48
= 36 + 48
= 84
 
Answer(s): 84