Michael had 50% more beads than Caleb. Joshua had 20% fewer beads than Michael. Michael and Caleb gave Joshua some beads in the ratio of 1 : 3. As a result, Joshua had 50% more beads than before. Given that Caleb had 225 less beads than Joshua in the end, how many beads did Caleb give to Joshua?

Michael	Caleb	Joshua
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Michael : Caleb = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Michael : Joshua = 5 : 4

The number of beads that Michael had at first is repeated. Make the number of beads that Michael had at first the same.  LCM of 3 and 5 is 15.

	Michael	Caleb	Joshua
Before	15x2 =  30 u	10x2 = 20 u	12x2 = 24 u
Change			+ 6x2 = + 12 u
Comparing the changes in the number of beads	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	27 u	11 u	18x2 = 36 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of beads that Michael and Caleb gave to Joshua is repeated.  Make the total number of beads that Michael and Caleb gave to Joshua the same.  LCM of 4 and 6 is 12.

Number of beads that Caleb had less than Joshua 
= 36 u - 11 u
= 25 u

25 u = 225

1 u = 225 ÷ 25 = 9

Number of beads that Caleb gave to Joshua
= 9 u
= 9 x 9
= 81

Answer(s): 81