Gillian, Winnie and Linda had a total of 68 cards. The ratio of Winnie's cards to Linda's cards was at first 10 : 9. After Gillian and Winnie each gave half of their cards away, the 3 children had 43 cards left. How many cards did Gillian and Winnie have at first?
| |
Gillian |
Winnie |
Linda |
Total |
| Before |
2 p |
10 u |
9 u |
68 |
| Change |
- 1 p |
- 5 u |
|
- 25 |
| After |
1 p |
5 u |
9 u |
43 |
Number of cards that Gillian and Winnie gave away
= 68 - 43
= 25
1 p + 5 u = 25
1 p = 25 - 5 u --- (1)
1 p + 5 u + 9 u = 43
1 p + 14 u = 43
1 p = 43 - 14 u --- (2)
(1) = (2)
25 - 5 u = 43 - 14 u
14 u - 5 u = 43 - 25
9 u = 18
1 u = 18 ÷ 9 = 2
From (1)
1 p = 25 - 5 u
1 p = 25 - 5 x 2
1 p = 25 - 10 = 15
Number of cards that Gillian and Winnie had at first
= 2 p + 10 u
= 2 x 15 + 10 x 2
= 30 + 18
= 48
Answer(s): 48
