The average number of playing cards Ethan and Riordan had was 443. The average number of playing cards Ethan and Michael had was 233. If the ratio of Riordan's playing cards to Michael's playing cards was 9 : 2, find the number of playing cards Ethan had.
Total number of cards that Ethan and Riordan had
= 2 x 443
= 886

Total number of cards that Ethan and Michael had
= 2 x 233
= 466

Number of playing cards Riordan had = 9 u
Number of playing cards Michael had = 2 u

Ethan's cards + 9 u = 886 --- (1)
Ethan's cards + 2 u = 466 --- (2)

(1) - (2)
9 u - 2 u = 886 - 466
7 u = 420
1 u = 420 ÷ 7 = 60

Number of playing cards that Michael had
= 2 u
= 2 x 60
= 120

Number of playing cards that Ethan had
= 466 - 120
= 346

Answer(s): 346