The average number of playing cards Michael and Riordan had was 428. The average number of playing cards Michael and Jack had was 223. If the ratio of Riordan's playing cards to Jack's playing cards was 9 : 4, find the number of playing cards Michael had.
Total number of cards that Michael and Riordan had
= 2 x 428
= 856

Total number of cards that Michael and Jack had
= 2 x 223
= 446

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

Michael's cards + 9 u = 856 --- (1)
Michael's cards + 4 u = 446 --- (2)

(1) - (2)
9 u - 4 u = 856 - 446
5 u = 410
1 u = 410 ÷ 5 = 82

Number of playing cards that Jack had
= 4 u
= 4 x 82
= 328

Number of playing cards that Michael had
= 446 - 328
= 118

Answer(s): 118