The average number of playing cards Caden and Michael had was 450. The average number of playing cards Caden and Neave had was 235. If the ratio of Michael's playing cards to Neave's playing cards was 7 : 2, find the number of playing cards Caden had.
Total number of cards that Caden and Michael had
= 2 x 450
= 900

Total number of cards that Caden and Neave had
= 2 x 235
= 470

Number of playing cards Michael had = 7 u
Number of playing cards Neave had = 2 u

Caden's cards + 7 u = 900 --- (1)
Caden's cards + 2 u = 470 --- (2)

(1) - (2)
7 u - 2 u = 900 - 470
5 u = 430
1 u = 430 ÷ 5 = 86

Number of playing cards that Neave had
= 2 u
= 2 x 86
= 172

Number of playing cards that Caden had
= 470 - 172
= 298

Answer(s): 298