The average number of playing cards Elijah and Japheth had was 426. The average number of playing cards Elijah and Vincent had was 228. If the ratio of Japheth's playing cards to Vincent's playing cards was 5 : 2, find the number of playing cards Elijah had.
Total number of cards that Elijah and Japheth had
= 2 x 426
= 852

Total number of cards that Elijah and Vincent had
= 2 x 228
= 456

Number of playing cards Japheth had = 5 u
Number of playing cards Vincent had = 2 u

Elijah's cards + 5 u = 852 --- (1)
Elijah's cards + 2 u = 456 --- (2)

(1) - (2)
5 u - 2 u = 852 - 456
3 u = 396
1 u = 396 ÷ 3 = 132

Number of playing cards that Vincent had
= 2 u
= 2 x 132
= 264

Number of playing cards that Elijah had
= 456 - 264
= 192

Answer(s): 192