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

Christian	Ella	Ryan
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Christian : Ella = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Christian : Ryan = 2 : 1

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

	Christian	Ella	Ryan
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 Christian and Ella gave to Ryan is repeated.  Make the total number of cards that Christian and Ella gave to Ryan the same.  LCM of 9 and 3 is 9.

Number of cards that Ella had less than Ryan 
= 24 u - 19 u
= 5 u

5 u = 50

1 u = 50 ÷ 5 = 10

Number of cards that Ella gave to Ryan
= 5 u
= 5 x 10
= 50

Answer(s): 50