The average number of playing cards Elijah and Will had was 465. The average number of playing cards Elijah and Oliver had was 225. If the ratio of Will's playing cards to Oliver's playing cards was 5 : 2, find the number of playing cards Elijah had.
Total number of cards that Elijah and Will had
= 2 x 465
= 930

Total number of cards that Elijah and Oliver had
= 2 x 225
= 450

Number of playing cards Will had = 5 u
Number of playing cards Oliver had = 2 u

Elijah's cards + 5 u = 930 --- (1)
Elijah's cards + 2 u = 450 --- (2)

(1) - (2)
5 u - 2 u = 930 - 450
3 u = 480
1 u = 480 ÷ 3 = 160

Number of playing cards that Oliver had
= 2 u
= 2 x 160
= 320

Number of playing cards that Elijah had
= 450 - 320
= 130

Answer(s): 130