Pierre and Paul had the same number of candy canes. Each of them packed his own candy canes into packets. Pierre packed 5 candy canes in each packet and had 4 candy canes left. Paul packed 8 candy canes in each packet and was short of 5 candy canes.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of candy canes each of them had if they used different number of packets?
| |
Pierre |
Paul |
| Number |
1 u |
1 u |
| Value |
5 |
8 |
| Total value |
5 u + 4 |
8 u - 5 |
The total number of candy canes that Pierre and Paul each had is the same.
8 u - 5 = 5 u + 4
8 u - 5 u = 5 + 4
3 u = 9
1 u = 9 ÷ 3 = 3
Number of packets that each had if they have used the same number of packets = 3
(b)
The number of packets that each had is different.
Multiples of 5: 5, 10, 15
Multiples of 5 (+4): 9, 14, 19
Multiples of 8: 8, 16, 24
Multiples of 8 (-5): 3, 11, 19
Smallest common number: 19
Pierre needs 3 packets of 5 candy canes and Paul needs 2 packets of 8 candy canes.
Smallest possible number of candy canes each of them had if they used different number of packets = 19
Answer(s): (a) 3; (b) 19
