Harry and Liam collected some erasers. If Harry gave Liam 54 erasers, both would have an equal number of erasers. If Liam gave Harry 40 erasers, Harry would have 5 times as many erasers as Liam. Find the number of erasers each of them had.
- Harry?
- Liam?
| Case 1 |
Case 2 |
| Harry |
Liam |
Harry |
Liam |
| 3 u + 54 |
3 u - 54 |
5 u - 40 |
1 u + 40 |
| - 54 |
+ 54 |
+ 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 Liam had at first is the same in both cases.
3 u - 54 = 1 u + 40
3 u - 1 u = 54 + 40
2 u = 94
1 u = 94 ÷ 2 = 47
Number of erasers that Harry had
= 3 u + 54
= 3 x 47 + 54
= 195
(b)
Number of erasers that Liam had
= 3 u - 54
= 3 x 47 - 54
= 87
Answer(s): (a) 195; (b) 87
