Vanessa, Winnie and Roshel had a total of 133 cards. The ratio of Winnie's cards to Roshel's cards was at first 8 : 5. After Vanessa and Winnie each gave half of their cards away, the 3 children had 84 cards left. How many cards did Vanessa and Roshel have at first?
| |
Vanessa |
Winnie |
Roshel |
Total |
| Before |
2 p |
8 u |
5 u |
133 |
| Change |
- 1 p |
- 4 u |
|
- 49 |
| After |
1 p |
4 u |
5 u |
84 |
Number of cards that Vanessa and Winnie gave away
= 133 - 84
= 49
1 p + 4 u = 49
1 p = 49 - 4 u --- (1)
1 p + 4 u + 5 u = 84
1 p + 9 u = 84
1 p = 84 - 9 u --- (2)
(1) = (2)
49 - 4 u = 84 - 9 u
9 u - 4 u = 84 - 49
5 u = 35
1 u = 35 ÷ 5 = 7
From (1)
1 p = 49 - 4 u
1 p = 49 - 4 x 7
1 p = 49 - 28 = 21
Number of cards that Vanessa and Roshel had at first
= 2 p + 5 u
= 2 x 21 + 5 x 7
= 42 + 35
= 77
Answer(s): 77
