Victoria and Luke collect cards and coins. Luke has 90 less cards than coins. Luke has 4 times the number of cards Victoria has, and Victoria has 20% more coins than Luke. After Victoria gives Luke all of her cards and Luke gives Victoria 60% of his coins, Luke has 32 less coins than cards. Find the number of coins Victoria has at first.

Victoria		Luke
Coins	Cards	Coins	Cards
4.8 u + 108	1 u	4 u + 90	4 u
+ 2.4 u + 54	- 1 u	- 2.4 u - 54	+ 1 u
7.2 u + 162	0	1.6 u + 36	5 u

100%+ 20% = 120% 

120% x 4 u
= ¹²⁰₁₀₀ x 4 u
= 4.8 u

120% x 90
= ¹²⁰₁₀₀ x 90
= 108 

60% x 4 u
= ⁶⁰₁₀₀ x 4 u
= 2.4 u  

60% x 90 
= ⁶⁰₁₀₀ x 90
= 54 

If another 32 coins are given to Luke, he will have equal number of coins and cards in the end.
5 u = 1.6 u + 36 + 32
5 u - 1.6 u = 68
3.4 u = 68

1 u = 68 ÷ 3.4 = 20

Number of coins that Victoria has at first
= 4.8 u + 108
= 4.8 x 20 + 108
= 96 + 108
= 204
 
Answer(s): 204