Michael had 40% more beads than Mia. Christopher had 20% fewer beads than Michael. Michael and Mia gave Christopher some beads in the ratio of 1 : 3. As a result, Christopher had 50% more beads than before. Given that Christopher had 275 more beads than Mia in the end, how many beads did Michael give to Christopher?

Michael	Mia	Christopher
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Michael : Mia = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Michael : Christopher = 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 7 and 5 is 35.

	Michael	Mia	Christopher
Before	35x2 =  70 u	25x2 = 50 u	28x2 = 56 u
Change			+ 14x2 = + 28 u
Comparing the changes in the number of beads	- 1x7 = - 7 u	- 3x7 = - 21 u	+ 4x7 = + 28 u
After	63 u	29 u	42x2 = 84 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of beads that Michael and Mia gave to Christopher is repeated.  Make the total number of beads that Michael and Mia gave to Christopher the same.  LCM of 4 and 14 is 28.

Number of beads that Christopher had more than Mia 
= 84 u - 29 u
= 55 u

55 u = 275

1 u = 275 ÷ 55 = 5

Number of beads that Michael gave to Christopher
= 7 u
= 7 x 5
= 35

Answer(s): 35