The average number of playing cards Oliver and Archie had was 433. The average number of playing cards Oliver and Elijah had was 233. If the ratio of Archie's playing cards to Elijah's playing cards was 9 : 4, find the number of playing cards Oliver had.
Total number of cards that Oliver and Archie had
= 2 x 433
= 866

Total number of cards that Oliver and Elijah had
= 2 x 233
= 466

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

Oliver's cards + 9 u = 866 --- (1)
Oliver's cards + 4 u = 466 --- (2)

(1) - (2)
9 u - 4 u = 866 - 466
5 u = 400
1 u = 400 ÷ 5 = 80

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

Number of playing cards that Oliver had
= 466 - 320
= 146

Answer(s): 146