Riordan and John had 84 marbles in total. John had 18 marbles more than Riordan at first. After Riordan and John played a game with Gabby, Riordan had ¹₃ as many marbles as John. If Riordan lost as many marbles as John to Gabby, find the number of marbles that Riordan lost to Gabby.

	Riordan	John	Difference
Before	1 u	1 u + 18	18
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of marbles at first
= 1 u + 1 u + 18 
= 2 u + 18

2 u + 18 = 84
2 u = 84 - 18
2 u = 66

1 u = 66 ÷ 2 = 33

Since Riordan lost the same number of marbles as John, the difference in the number of marbles between Riordan and John at first and in the end remains the same.

Difference in the number of marbles in the end
= 3 p - 1 p
= 2 p

2 p = 18

1 p = 18 ÷ 2 = 9

Number of marbles that Riordan lost to Gabby
= 1 u - 1 p
= 33 - 1 x 9
= 33 - 9
= 24

Answer(s): 24