Elijah, Jeremy and Neave had a total of 24 cards. The ratio of Jeremy's cards to Neave's cards was 2 : 3 at first. Elijah and Jeremy each gave away
12 of their cards. Given that the three boys had 15 cards left, how many cards did Elijah have in the end?
|
Elijah |
Jeremy |
Neave |
Total |
Comparing Jeremy and Neave at first |
|
2 u |
3 u |
|
Before |
2 p |
2x1 = 2 u |
3 u |
24 |
Change |
- 1 p |
-1x1 = - 1 u |
|
- 9 |
After |
1 p |
1x1 = 1 u |
3 u |
15 |
Total number of cards that Elijah and Jeremy gave away
= 24 - 15
= 9
The number of cards that Jeremy had at first is repeated. Make the number of cards that Jeremy had at first the same. LCM of 2 and 2 is 2.
1 p + 1 u = 24 - 15
1 p + 1 u = 9
1 p = 9 - 1 u --- (1)
1 p + 1 u + 3 u = 15
1 p + 4 u = 15
1 p = 15 - 4 u --- (2)
(1) = (2)
9 - 1 u = 15 - 4 u
4 u - 1 u = 15 - 9
4 u - 1 u = 6
3 u = 6
1 u = 6 ÷ 3 = 2
Substitute 1 u = 2 into (1).
1 p = 9 - 1 u
1 p = 9 - 1 x 2
1 p = 9 - 2
1 p = 7
Number of cards that Elijah had in the end
= 1 p
= 7
Answer(s): 7