Will and Julian collected some cards. If Will gave Julian 62 cards, both would have an equal number of cards. If Julian gave Will 31 cards, Will would have 4 times as many cards as Julian. Find the number of cards each of them had.
- Will?
- Julian?
| Case 1 |
Case 2 |
| Will |
Julian |
Will |
Julian |
| 5 u + 62 |
5 u - 62 |
8 u - 31 |
2 u + 31 |
| - 62 |
+ 62 |
+ 31 |
- 31 |
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 Julian had at first is the same in both cases.
5 u - 62 = 2 u + 31
5 u - 2 u = 62 + 31
3 u = 93
1 u = 93 ÷ 3 = 31
Number of cards that Will had
= 5 u + 62
= 5 x 31 + 62
= 217
(b)
Number of cards that Julian had
= 5 u - 62
= 5 x 31 - 62
= 93
Answer(s): (a) 217; (b) 93
