Cody, Elijah and Glen had a total of 59 cards. The ratio of the number of cards that Elijah had to the number of cards that Glen had was 6 : 5. After Cody and Elijah each gave away half of their cards, the 3 children had 42 cards left. How many cards did Elijah and Glen have at first?
| |
Cody |
Elijah |
Glen |
Total |
| Before |
2 p |
6 u |
5 u |
59 |
| Change |
- 1 p |
- 3 u |
|
- 17 |
| After |
1 p |
3 u |
5 u |
42 |
Total number of cards that Cody and Elijah gave away
= 59 - 42
= 17
1 p + 3 u = 17 --- (1)
1 p + 3 u + 5 u = 42
1 p + 8 u = 42 --- (2)
(2) - (1)
(1 p + 8 u) - (1 p + 3 u) = 42 - 17
8 u - 3 u = 25
5 u = 25
1 u = 25 ÷ 5 = 5
Total number of cards that Elijah and Glen had at first
= 6 u + 5 u
= 11 u
= 11 x 5
= 55
Answer(s): 55
