Hannah had 20% more beads than Jayden. Chloe had 40% fewer beads than Hannah. Hannah and Jayden gave Chloe some beads in the ratio of 1 : 5. As a result, Chloe had 50% more beads than before. Given that Jayden had 228 less beads than Chloe in the end, how many beads did Jayden give to Chloe?

Hannah	Jayden	Chloe
6x5	5x5
5x6		3x6
30	25	18

100% + 20% = 120%
120% = ¹²⁰₁₀₀ = ⁶₅

Hannah : Jayden = 6 : 5

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

Hannah : Chloe = 5 : 3

The number of beads that Hannah had at first is repeated. Make the number of beads that Hannah had at first the same.  LCM of 6 and 5 is 30.

	Hannah	Jayden	Chloe
Before	30x2 =  60 u	25x2 = 50 u	18x2 = 36 u
Change			+ 9x2 = + 18 u
Comparing the changes in the number of beads	- 1x3 = - 3 u	- 5x3 = - 15 u	+ 6x3 = + 18 u
After	57 u	35 u	27x2 = 54 u

50% x 18 
= ⁵⁰₁₀₀ x 18 
= 9 

The total number of beads that Hannah and Jayden gave to Chloe is repeated.  Make the total number of beads that Hannah and Jayden gave to Chloe the same.  LCM of 6 and 9 is 18.

Number of beads that Jayden had less than Chloe 
= 54 u - 35 u
= 19 u

19 u = 228

1 u = 228 ÷ 19 = 12

Number of beads that Jayden gave to Chloe
= 15 u
= 15 x 12
= 180

Answer(s): 180