Eric, Cole and Vaidev had a total of 89 cards. The ratio of the number of cards that Cole had to the number of cards that Vaidev had was 2 : 9. After Eric and Cole each gave away half of their cards, the 3 children had 76 cards left. How many cards did Cole and Vaidev have at first?
| |
Eric |
Cole |
Vaidev |
Total |
| Before |
2 p |
2 u |
9 u |
89 |
| Change |
- 1 p |
- 1 u |
|
- 13 |
| After |
1 p |
1 u |
9 u |
76 |
Total number of cards that Eric and Cole gave away
= 89 - 76
= 13
1 p + 1 u = 13 --- (1)
1 p + 1 u + 9 u = 76
1 p + 10 u = 76 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 1 u) = 76 - 13
10 u - 1 u = 63
9 u = 63
1 u = 63 ÷ 9 = 7
Total number of cards that Cole and Vaidev had at first
= 2 u + 9 u
= 11 u
= 11 x 7
= 77
Answer(s): 77
