The average number of playing cards Vincent and Riordan had was 478. The average number of playing cards Vincent and Ian had was 220. If the ratio of Riordan's playing cards to Ian's playing cards was 5 : 2, find the number of playing cards Vincent had.
Total number of cards that Vincent and Riordan had
= 2 x 478
= 956

Total number of cards that Vincent and Ian had
= 2 x 220
= 440

Number of playing cards Riordan had = 5 u
Number of playing cards Ian had = 2 u

Vincent's cards + 5 u = 956 --- (1)
Vincent's cards + 2 u = 440 --- (2)

(1) - (2)
5 u - 2 u = 956 - 440
3 u = 516
1 u = 516 ÷ 3 = 172

Number of playing cards that Ian had
= 2 u
= 2 x 172
= 344

Number of playing cards that Vincent had
= 440 - 344
= 96

Answer(s): 96