Luke and Oscar collected some stickers. If Luke gave Oscar 66 stickers, both would have an equal number of stickers. If Oscar gave Luke 40 stickers, Luke would have 5 times as many stickers as Oscar. Find the number of stickers each of them had.
- Luke?
- Oscar?
| Case 1 |
Case 2 |
| Luke |
Oscar |
Luke |
Oscar |
| 3 u + 66 |
3 u - 66 |
5 u - 40 |
1 u + 40 |
| - 66 |
+ 66 |
+ 40 |
- 40 |
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 stickers the same. LCM of 2 and 6 is 6.
The number of stickers that Oscar had at first is the same in both cases.
3 u - 66 = 1 u + 40
3 u - 1 u = 66 + 40
2 u = 106
1 u = 106 ÷ 2 = 53
Number of stickers that Luke had
= 3 u + 66
= 3 x 53 + 66
= 225
(b)
Number of stickers that Oscar had
= 3 u - 66
= 3 x 53 - 66
= 93
Answer(s): (a) 225; (b) 93
