The average number of playing cards Gabriel and Howard had was 454. The average number of playing cards Gabriel and Eric had was 239. If the ratio of Howard's playing cards to Eric's playing cards was 7 : 2, find the number of playing cards Gabriel had.
Total number of cards that Gabriel and Howard had
= 2 x 454
= 908

Total number of cards that Gabriel and Eric had
= 2 x 239
= 478

Number of playing cards Howard had = 7 u
Number of playing cards Eric had = 2 u

Gabriel's cards + 7 u = 908 --- (1)
Gabriel's cards + 2 u = 478 --- (2)

(1) - (2)
7 u - 2 u = 908 - 478
5 u = 430
1 u = 430 ÷ 5 = 86

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

Number of playing cards that Gabriel had
= 478 - 172
= 306

Answer(s): 306