Kathy, Zoe and Winnie had a total of 110 cards. The ratio of Zoe's cards to Winnie's cards was at first 4 : 3. After Kathy and Zoe each gave half of their cards away, the 3 children had 73 cards left. How many cards did Kathy and Winnie have at first?
| |
Kathy |
Zoe |
Winnie |
Total |
| Before |
2 p |
4 u |
3 u |
110 |
| Change |
- 1 p |
- 2 u |
|
- 37 |
| After |
1 p |
2 u |
3 u |
73 |
Number of cards that Kathy and Zoe gave away
= 110 - 73
= 37
1 p + 2 u = 37
1 p = 37 - 2 u --- (1)
1 p + 2 u + 3 u = 73
1 p + 5 u = 73
1 p = 73 - 5 u --- (2)
(1) = (2)
37 - 2 u = 73 - 5 u
5 u - 2 u = 73 - 37
3 u = 36
1 u = 36 ÷ 3 = 12
From (1)
1 p = 37 - 2 u
1 p = 37 - 2 x 12
1 p = 37 - 24 = 13
Number of cards that Kathy and Winnie had at first
= 2 p + 3 u
= 2 x 13 + 3 x 12
= 26 + 36
= 62
Answer(s): 62
