Julian had 40% more beads than Owen. Roshel had 20% fewer beads than Julian. Julian and Owen gave Roshel some beads in the ratio of 3 : 4. As a result, Roshel had 50% more beads than before. Given that Owen had 300 less beads than Roshel in the end, how many beads did Owen give to Roshel?

Julian	Owen	Roshel
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Julian : Owen = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Julian : Roshel = 5 : 4

The number of beads that Julian had at first is repeated. Make the number of beads that Julian had at first the same.  LCM of 7 and 5 is 35.

	Julian	Owen	Roshel
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of beads	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of beads that Julian and Owen gave to Roshel is repeated.  Make the total number of beads that Julian and Owen gave to Roshel the same.  LCM of 7 and 14 is 14.

Number of beads that Owen had less than Roshel 
= 42 u - 17 u
= 25 u

25 u = 300

1 u = 300 ÷ 25 = 12

Number of beads that Owen gave to Roshel
= 8 u
= 8 x 12
= 96

Answer(s): 96