Pierre and Henry collected some erasers. If Pierre gave Henry 61 erasers, both would have an equal number of erasers. If Henry gave Pierre 37 erasers, Pierre would have 5 times as many erasers as Henry. Find the number of erasers each of them had.
- Pierre?
- Henry?
| Case 1 |
Case 2 |
| Pierre |
Henry |
Pierre |
Henry |
| 3 u + 61 |
3 u - 61 |
5 u - 37 |
1 u + 37 |
| - 61 |
+ 61 |
+ 37 |
- 37 |
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 Henry had at first is the same in both cases.
3 u - 61 = 1 u + 37
3 u - 1 u = 61 + 37
2 u = 98
1 u = 98 ÷ 2 = 49
Number of erasers that Pierre had
= 3 u + 61
= 3 x 49 + 61
= 208
(b)
Number of erasers that Henry had
= 3 u - 61
= 3 x 49 - 61
= 86
Answer(s): (a) 208; (b) 86
