Hazel and Ethan collect coins and pens. Ethan has 48 less coins than pens. Ethan has 3 times the number of coins Hazel has, and Hazel has 25% more pens than Ethan. After Hazel gives Ethan all of her coins and Ethan gives Hazel 75% of his pens, Ethan has 27 more coins than pens. Find the number of pens Hazel has at first.

Hazel		Ethan
Pens	Coins	Pens	Coins
3.75 u + 60	1 u	3 u + 48	3 u
+ 2.25 u + 36	- 1 u	- 2.25 u - 36	+ 1 u
6 u + 96	0	0.75 u + 12	4 u

100%+ 25% = 125% 

125% x 3 u
= ¹²⁵₁₀₀ x 3 u
= 3.75 u

125% x 48
= ¹²⁵₁₀₀ x 48
= 60 

75% x 3 u
= ⁷⁵₁₀₀ x 3 u
= 2.25 u  

75% x 48 
= ⁷⁵₁₀₀ x 48
= 36 

If another 27 pens are given to Ethan, he will have equal number of pens and coins in the end.
4 u = 0.75 u + 12 + 27
4 u - 0.75 u = 39
3.25 u = 39

1 u = 39 ÷ 3.25 = 12

Number of pens that Hazel has at first
= 3.75 u + 60
= 3.75 x 12 + 60
= 45 + 60
= 105
 
Answer(s): 105