Jeremy, Bobby and Vincent had some beads. Bobby had 60% more beads than Jeremy. Bobby had ²₇ of Vincent's. After Jeremy gave 6 beads to Bobby, he had ¹₂ of what Bobby had. How many more beads did Vincent have than Bobby in the end?

Jeremy	Bobby	Vincent
5x1	8x1
	2x4	7x4
5	8	28

	Vincent	Jeremy	Bobby	Total beads of  Jeremy and Bobby
Before	28x3 = 84 u	5x3 = 15 u	8x3 = 24 u	13x3 = 39 u
Change		- 6	+ 6
After	84 u	1x13 = 13 u	2x13 = 26 u	3x13 = 39 u

Number of beads that Bobby had more than Jeremy at first in percent
= 100%+ 60%
= 160%

160% = ¹⁶⁰₁₀₀ = ⁸₅

Jeremy : Bobby = 5 : 8

The number of beads that Bobby had at first is repeated.  Make the number of beads that Bobby had at first the same.  LCM of 8 and 2 is 8.

When Jeremy gave 6 beads to Bobby, the total number of beads that Bobby and Jeremy had at first and in the end remains the same.  Make the total number of beads that Bobby and Jeremy had the same.  LCM of 13 and 3 is 39.

Number of beads that Jeremy gave to Bobby
= 15 u - 13 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

Number of beads that Vincent had more than Bobby in the end
= 84 u - 26 u
= 58 u
= 58 x 3
= 174

Answer(s): 174