Vincent and Peter collected some cards. If Vincent gave Peter 63 cards, both would have an equal number of cards. If Peter gave Vincent 42 cards, Vincent would have 6 times as many cards as Peter. Find the number of cards each of them had.
- Vincent?
- Peter?
| Case 1 |
Case 2 |
| Vincent |
Peter |
Vincent |
Peter |
| 7 u + 63 |
7 u - 63 |
12 u - 42 |
2 u + 42 |
| - 63 |
+ 63 |
+ 42 |
- 42 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of cards the same. LCM of 2 and 7 is 14.
The number of cards that Peter had at first is the same in both cases.
7 u - 63 = 2 u + 42
7 u - 2 u = 63 + 42
5 u = 105
1 u = 105 ÷ 5 = 21
Number of cards that Vincent had
= 7 u + 63
= 7 x 21 + 63
= 210
(b)
Number of cards that Peter had
= 7 u - 63
= 7 x 21 - 63
= 84
Answer(s): (a) 210; (b) 84
