The average number of playing cards Dylan and Elijah had was 423. The average number of playing cards Dylan and Howard had was 223. If the ratio of Elijah's playing cards to Howard's playing cards was 9 : 4, find the number of playing cards Dylan had.
Total number of cards that Dylan and Elijah had
= 2 x 423
= 846

Total number of cards that Dylan and Howard had
= 2 x 223
= 446

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

Dylan's cards + 9 u = 846 --- (1)
Dylan's cards + 4 u = 446 --- (2)

(1) - (2)
9 u - 4 u = 846 - 446
5 u = 400
1 u = 400 ÷ 5 = 80

Number of playing cards that Howard had
= 4 u
= 4 x 80
= 320

Number of playing cards that Dylan had
= 446 - 320
= 126

Answer(s): 126