The average number of playing cards Mark and Riordan had was 460. The average number of playing cards Mark and Elijah had was 225. If the ratio of Riordan's playing cards to Elijah's playing cards was 9 : 4, find the number of playing cards Mark had.
Total number of cards that Mark and Riordan had
= 2 x 460
= 920

Total number of cards that Mark and Elijah had
= 2 x 225
= 450

Number of playing cards Riordan had = 9 u
Number of playing cards Elijah had = 4 u

Mark's cards + 9 u = 920 --- (1)
Mark's cards + 4 u = 450 --- (2)

(1) - (2)
9 u - 4 u = 920 - 450
5 u = 470
1 u = 470 ÷ 5 = 94

Number of playing cards that Elijah had
= 4 u
= 4 x 94
= 376

Number of playing cards that Mark had
= 450 - 376
= 74

Answer(s): 74