Will and Justin collected some cards. If Will gave Justin 63 cards, both would have an equal number of cards. If Justin gave Will 30 cards, Will would have 4 times as many cards as Justin. Find the number of cards each of them had.
- Will?
- Justin?
| Case 1 |
Case 2 |
| Will |
Justin |
Will |
Justin |
| 5 u + 63 |
5 u - 63 |
8 u - 30 |
2 u + 30 |
| - 63 |
+ 63 |
+ 30 |
- 30 |
1x5 =
5 u |
1x5 =
5 u |
4x2 =
8 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 5 is 10.
The number of cards that Justin had at first is the same in both cases.
5 u - 63 = 2 u + 30
5 u - 2 u = 63 + 30
3 u = 93
1 u = 93 ÷ 3 = 31
Number of cards that Will had
= 5 u + 63
= 5 x 31 + 63
= 218
(b)
Number of cards that Justin had
= 5 u - 63
= 5 x 31 - 63
= 92
Answer(s): (a) 218; (b) 92
