Ethan and Luke collected some erasers. If Ethan gave Luke 68 erasers, both would have an equal number of erasers. If Luke gave Ethan 40 erasers, Ethan would have 5 times as many erasers as Luke. Find the number of erasers each of them had.
- Ethan?
- Luke?
| Case 1 |
Case 2 |
| Ethan |
Luke |
Ethan |
Luke |
| 3 u + 68 |
3 u - 68 |
5 u - 40 |
1 u + 40 |
| - 68 |
+ 68 |
+ 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 erasers the same. LCM of 2 and 6 is 6.
The number of erasers that Luke had at first is the same in both cases.
3 u - 68 = 1 u + 40
3 u - 1 u = 68 + 40
2 u = 108
1 u = 108 ÷ 2 = 54
Number of erasers that Ethan had
= 3 u + 68
= 3 x 54 + 68
= 230
(b)
Number of erasers that Luke had
= 3 u - 68
= 3 x 54 - 68
= 94
Answer(s): (a) 230; (b) 94
