Ben and Simon collected some erasers. If Ben gave Simon 54 erasers, both would have an equal number of erasers. If Simon gave Ben 36 erasers, Ben would have 5 times as many erasers as Simon. Find the number of erasers each of them had.
- Ben?
- Simon?
| Case 1 |
Case 2 |
| Ben |
Simon |
Ben |
Simon |
| 3 u + 54 |
3 u - 54 |
5 u - 36 |
1 u + 36 |
| - 54 |
+ 54 |
+ 36 |
- 36 |
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 Simon had at first is the same in both cases.
3 u - 54 = 1 u + 36
3 u - 1 u = 54 + 36
2 u = 90
1 u = 90 ÷ 2 = 45
Number of erasers that Ben had
= 3 u + 54
= 3 x 45 + 54
= 189
(b)
Number of erasers that Simon had
= 3 u - 54
= 3 x 45 - 54
= 81
Answer(s): (a) 189; (b) 81
