Usha and Vincent collect pencils and coins. Vincent has 100 less pencils than coins. Vincent has 5 times the number of pencils Usha has, and Usha has 30% more coins than Vincent. After Usha gives Vincent all of her pencils and Vincent gives Usha 70% of his coins, Vincent has 6 more pencils than coins. Find the number of coins Usha has at first.

Usha		Vincent
Coins	Pencils	Coins	Pencils
6.5 u + 130	1 u	5 u + 100	5 u
+ 3.5 u + 70	- 1 u	- 3.5 u - 70	+ 1 u
10 u + 200	0	1.5 u + 30	6 u

100%+ 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 100
= ¹³⁰₁₀₀ x 100
= 130 

70% x 5 u
= ⁷⁰₁₀₀ x 5 u
= 3.5 u  

70% x 100 
= ⁷⁰₁₀₀ x 100
= 70 

If another 6 coins are given to Vincent, he will have equal number of coins and pencils in the end.
6 u = 1.5 u + 30 + 6
6 u - 1.5 u = 36
4.5 u = 36

1 u = 36 ÷ 4.5 = 8

Number of coins that Usha has at first
= 6.5 u + 130
= 6.5 x 8 + 130
= 52 + 130
= 182
 
Answer(s): 182