John and Reggie collected some erasers. If John gave Reggie 50 erasers, both would have an equal number of erasers. If Reggie gave John 36 erasers, John would have 5 times as many erasers as Reggie. Find the number of erasers each of them had.
- John?
- Reggie?
| Case 1 |
Case 2 |
| John |
Reggie |
John |
Reggie |
| 3 u + 50 |
3 u - 50 |
5 u - 36 |
1 u + 36 |
| - 50 |
+ 50 |
+ 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 Reggie had at first is the same in both cases.
3 u - 50 = 1 u + 36
3 u - 1 u = 50 + 36
2 u = 86
1 u = 86 ÷ 2 = 43
Number of erasers that John had
= 3 u + 50
= 3 x 43 + 50
= 179
(b)
Number of erasers that Reggie had
= 3 u - 50
= 3 x 43 - 50
= 79
Answer(s): (a) 179; (b) 79
