Samuel had 50% more cards than Jamie. Riordan had 20% fewer cards than Samuel. Samuel and Jamie gave Riordan some cards in the ratio of 1 : 3. As a result, Riordan had 25% more cards than before. Given that Jamie had 261 less cards than Riordan in the end, how many cards did Jamie give to Riordan?

Samuel	Jamie	Riordan
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Samuel : Jamie = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Samuel : Riordan = 5 : 4

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

	Samuel	Jamie	Riordan
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of cards	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	57 u	31 u	15x4 = 60 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of cards that Samuel and Jamie gave to Riordan is repeated.  Make the total number of cards that Samuel and Jamie gave to Riordan the same.  LCM of 4 and 3 is 12.

Number of cards that Jamie had less than Riordan 
= 60 u - 31 u
= 29 u

29 u = 261

1 u = 261 ÷ 29 = 9

Number of cards that Jamie gave to Riordan
= 9 u
= 9 x 9
= 81

Answer(s): 81