Charlie, Ivan and Ethan had a total of 74 cards. The ratio of the number of cards that Ivan had to the number of cards that Ethan had was 8 : 7. After Charlie and Ivan each gave away half of their cards, the 3 children had 51 cards left. How many cards did Ivan and Ethan have in the end?
| |
Charlie |
Ivan |
Ethan |
Total |
| Before |
2 p |
8 u |
7 u |
74 |
| Change |
- 1 p |
- 4 u |
|
- 23 |
| After |
1 p |
4 u |
7 u |
51 |
Total number of cards that Charlie and Ivan gave away
= 74 - 51
= 23
1 p + 4 u = 23 --- (1)
1 p + 4 u + 7 u = 51
1 p + 11 u = 51 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 51 - 23
11 u - 4 u = 28
7 u = 28
1 u = 28 ÷ 7 = 4
Total number of cards that Ivan and Ethan had in the end
= 4 u + 7 u
= 11 u
= 11 x 4
= 44
Answer(s): 44
