Kathy and Luke collect pens and coins. Luke has 95 more coins than pens. Luke has 3 times the number of pens Kathy has, and Kathy has 40% more coins than Luke. After Kathy gives Luke all of her pens and Luke gives Kathy 60% of his coins, Luke has 18 more pens than coins. Find the number of coins Kathy has at first.

Kathy		Luke
Coins	Pens	Coins	Pens
4.2 u + 133	1 u	3 u + 95	3 u
+ 1.8 u + 57	- 1 u	- 1.8 u - 57	+ 1 u
6 u + 190	0	1.2 u + 38	4 u

100% + 40% = 140% 

140% x 3 u
= ¹⁴⁰₁₀₀ x 3 u
= 4.2 u

140% x 95
= ¹⁴⁰₁₀₀ x 95
= 133 

60% x 3 u
= ⁶⁰₁₀₀ x 3 u
= 1.8 u  

60% x 95 
= ⁶⁰₁₀₀ x 95
= 57 

If another 18 coins are given to Luke, he will have equal number of coins and pens in the end.
4 u = 1.2 u + 38 + 18
4 u - 1.2 u = 56
2.8 u = 56

1 u = 56 ÷ 2.8 = 20

Number of coins that Kathy has at first
= 4.2 u + 133
= 4.2 x 20 + 133
= 84 + 133
= 217
 
Answer(s): 217