Fred, Brandon and Nick had some beads. Brandon had 25% more beads than Fred. Brandon had ²₇ of Nick's. After Fred gave 45 beads to Brandon, he had ¹₅ of what Brandon had. How many more beads did Nick have than Brandon in the end?

Fred	Brandon	Nick
4x2	5x2
	2x5	7x5
8	10	35

	Nick	Fred	Brandon	Total beads of  Fred and Brandon
Before	35x1 = 35 u	8x1 = 8 u	10x1 = 10 u	18x1 = 18 u
Change		- 45	+ 45
After	35 u	1x3 = 3 u	5x3 = 15 u	6x3 = 18 u

Number of beads that Brandon had more than Fred at first in percent
= 100%+ 25%
= 125%

125% = ¹²⁵₁₀₀ = ⁵₄

Fred : Brandon = 4 : 5

The number of beads that Brandon had at first is repeated.  Make the number of beads that Brandon had at first the same.  LCM of 5 and 2 is 10.

When Fred gave 45 beads to Brandon, the total number of beads that Brandon and Fred had at first and in the end remains the same.  Make the total number of beads that Brandon and Fred had the same.  LCM of 18 and 6 is 18.

Number of beads that Fred gave to Brandon
= 8 u - 3 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of beads that Nick had more than Brandon in the end
= 35 u - 15 u
= 20 u
= 20 x 9
= 180

Answer(s): 180