Andy and Justin collected some cards. If Andy gave Justin 59 cards, both would have an equal number of cards. If Justin gave Andy 33 cards, Andy would have 5 times as many cards as Justin. Find the number of cards each of them had.
- Andy?
- Justin?
| Case 1 |
Case 2 |
| Andy |
Justin |
Andy |
Justin |
| 3 u + 59 |
3 u - 59 |
5 u - 33 |
1 u + 33 |
| - 59 |
+ 59 |
+ 33 |
- 33 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of cards the same. LCM of 2 and 6 is 6.
The number of cards that Justin had at first is the same in both cases.
3 u - 59 = 1 u + 33
3 u - 1 u = 59 + 33
2 u = 92
1 u = 92 ÷ 2 = 46
Number of cards that Andy had
= 3 u + 59
= 3 x 46 + 59
= 197
(b)
Number of cards that Justin had
= 3 u - 59
= 3 x 46 - 59
= 79
Answer(s): (a) 197; (b) 79
