Gem and Vincent collect coins and beads. Vincent has 40 less coins than beads. Vincent has 5 times the number of coins Gem has, and Gem has 30% more beads than Vincent. After Gem gives Vincent all of her coins and Vincent gives Gem 70% of his beads, Vincent has 69 less beads than coins. Find the number of beads Gem has at first.

Gem		Vincent
Beads	Coins	Beads	Coins
6.5 u + 52	1 u	5 u + 40	5 u
+ 3.5 u + 28	- 1 u	- 3.5 u - 28	+ 1 u
10 u + 80	0	1.5 u + 12	6 u

100%+ 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 40
= ¹³⁰₁₀₀ x 40
= 52 

70% x 5 u
= ⁷⁰₁₀₀ x 5 u
= 3.5 u  

70% x 40 
= ⁷⁰₁₀₀ x 40
= 28 

If another 69 beads are given to Vincent, he will have equal number of beads and coins in the end.
6 u = 1.5 u + 12 + 69
6 u - 1.5 u = 81
4.5 u = 81

1 u = 81 ÷ 4.5 = 18

Number of beads that Gem has at first
= 6.5 u + 52
= 6.5 x 18 + 52
= 117 + 52
= 169
 
Answer(s): 169