Owen and Zeph collected some erasers. If Owen gave Zeph 61 erasers, both would have an equal number of erasers. If Zeph gave Owen 44 erasers, Owen would have 4 times as many erasers as Zeph. Find the number of erasers each of them had.
- Owen?
- Zeph?
| Case 1 |
Case 2 |
| Owen |
Zeph |
Owen |
Zeph |
| 5 u + 61 |
5 u - 61 |
8 u - 44 |
2 u + 44 |
| - 61 |
+ 61 |
+ 44 |
- 44 |
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 erasers the same. LCM of 2 and 5 is 10.
The number of erasers that Zeph had at first is the same in both cases.
5 u - 61 = 2 u + 44
5 u - 2 u = 61 + 44
3 u = 105
1 u = 105 ÷ 3 = 35
Number of erasers that Owen had
= 5 u + 61
= 5 x 35 + 61
= 236
(b)
Number of erasers that Zeph had
= 5 u - 61
= 5 x 35 - 61
= 114
Answer(s): (a) 236; (b) 114
