Japheth and Cody collected some erasers. If Japheth gave Cody 66 erasers, both would have an equal number of erasers. If Cody gave Japheth 39 erasers, Japheth would have 4 times as many erasers as Cody. Find the number of erasers each of them had.
- Japheth?
- Cody?
| Case 1 |
Case 2 |
| Japheth |
Cody |
Japheth |
Cody |
| 5 u + 66 |
5 u - 66 |
8 u - 39 |
2 u + 39 |
| - 66 |
+ 66 |
+ 39 |
- 39 |
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 Cody had at first is the same in both cases.
5 u - 66 = 2 u + 39
5 u - 2 u = 66 + 39
3 u = 105
1 u = 105 ÷ 3 = 35
Number of erasers that Japheth had
= 5 u + 66
= 5 x 35 + 66
= 241
(b)
Number of erasers that Cody had
= 5 u - 66
= 5 x 35 - 66
= 109
Answer(s): (a) 241; (b) 109
