Harry and Jenson collected some erasers. If Harry gave Jenson 65 erasers, both would have an equal number of erasers. If Jenson gave Harry 34 erasers, Harry would have 4 times as many erasers as Jenson. Find the number of erasers each of them had.
- Harry?
- Jenson?
| Case 1 |
Case 2 |
| Harry |
Jenson |
Harry |
Jenson |
| 5 u + 65 |
5 u - 65 |
8 u - 34 |
2 u + 34 |
| - 65 |
+ 65 |
+ 34 |
- 34 |
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 Jenson had at first is the same in both cases.
5 u - 65 = 2 u + 34
5 u - 2 u = 65 + 34
3 u = 99
1 u = 99 ÷ 3 = 33
Number of erasers that Harry had
= 5 u + 65
= 5 x 33 + 65
= 230
(b)
Number of erasers that Jenson had
= 5 u - 65
= 5 x 33 - 65
= 100
Answer(s): (a) 230; (b) 100
