Neave and Fabian collected some erasers. If Neave gave Fabian 64 erasers, both would have an equal number of erasers. If Fabian gave Neave 32 erasers, Neave would have 4 times as many erasers as Fabian. Find the number of erasers each of them had.
- Neave?
- Fabian?
| Case 1 |
Case 2 |
| Neave |
Fabian |
Neave |
Fabian |
| 5 u + 64 |
5 u - 64 |
8 u - 32 |
2 u + 32 |
| - 64 |
+ 64 |
+ 32 |
- 32 |
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 Fabian had at first is the same in both cases.
5 u - 64 = 2 u + 32
5 u - 2 u = 64 + 32
3 u = 96
1 u = 96 ÷ 3 = 32
Number of erasers that Neave had
= 5 u + 64
= 5 x 32 + 64
= 224
(b)
Number of erasers that Fabian had
= 5 u - 64
= 5 x 32 - 64
= 96
Answer(s): (a) 224; (b) 96
