Anna had 50% more marbles than Aubrey. Riordan had 20% fewer marbles than Anna. Anna and Aubrey gave Riordan some marbles in the ratio of 3 : 5. As a result, Riordan had 50% more marbles than before. Given that Riordan had 282 more marbles than Aubrey in the end, how many marbles did Anna give to Riordan?

Anna	Aubrey	Riordan
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Anna : Aubrey = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Anna : Riordan = 5 : 4

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

	Anna	Aubrey	Riordan
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 6x4 = + 24 u
Comparing the changes in the number of marbles	- 3x3 = - 9 u	- 5x3 = - 15 u	+ 8x3 = + 24 u
After	51 u	25 u	18x4 = 72 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of marbles that Anna and Aubrey gave to Riordan is repeated.  Make the total number of marbles that Anna and Aubrey gave to Riordan the same.  LCM of 8 and 6 is 24.

Number of marbles that Riordan had more than Aubrey 
= 72 u - 25 u
= 47 u

47 u = 282

1 u = 282 ÷ 47 = 6

Number of marbles that Anna gave to Riordan
= 9 u
= 9 x 6
= 54

Answer(s): 54