Michael had 25% more cards than Rebecca. Hannah had 50% fewer cards than Michael. Michael and Rebecca gave Hannah some cards in the ratio of 4 : 5. As a result, Hannah had 60% more cards than before. Given that Hannah had 40 more cards than Rebecca in the end, how many cards did Michael give to Hannah?

Michael	Rebecca	Hannah
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Michael : Rebecca = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Michael : Hannah = 2 : 1

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

	Michael	Rebecca	Hannah
Before	10x3 =  30 u	8x3 = 24 u	5x3 = 15 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of cards	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	26 u	19 u	8x3 = 24 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of cards that Michael and Rebecca gave to Hannah is repeated.  Make the total number of cards that Michael and Rebecca gave to Hannah the same.  LCM of 9 and 3 is 9.

Number of cards that Hannah had more than Rebecca 
= 24 u - 19 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Number of cards that Michael gave to Hannah
= 4 u
= 4 x 8
= 32

Answer(s): 32