Emma and Japheth collect buttons and coins. Japheth has 30 less buttons than coins. Japheth has 2 times the number of buttons Emma has, and Emma has 40% more coins than Japheth. After Emma gives Japheth all of her buttons and Japheth gives Emma 60% of his coins, Japheth has 21 more buttons than coins. Find the number of coins Emma has at first.

Emma		Japheth
Coins	Buttons	Coins	Buttons
2.8 u + 42	1 u	2 u + 30	2 u
+ 1.2 u + 18	- 1 u	- 1.2 u - 18	+ 1 u
4 u + 60	0	0.8 u + 12	3 u

100%+ 40% = 140% 

140% x 2 u
= ¹⁴⁰₁₀₀ x 2 u
= 2.8 u

140% x 30
= ¹⁴⁰₁₀₀ x 30
= 42 

60% x 2 u
= ⁶⁰₁₀₀ x 2 u
= 1.2 u  

60% x 30 
= ⁶⁰₁₀₀ x 30
= 18 

If another 21 coins are given to Japheth, he will have equal number of coins and buttons in the end.
3 u = 0.8 u + 12 + 21
3 u - 0.8 u = 33
2.2 u = 33

1 u = 33 ÷ 2.2 = 15

Number of coins that Emma has at first
= 2.8 u + 42
= 2.8 x 15 + 42
= 42 + 42
= 84
 
Answer(s): 84