Riordan and Julian had the same number of candy canes. Each of them packed his own candy canes into packets. Riordan packed 6 candy canes in each packet and had 4 candy canes left. Julian packed 9 candy canes in each packet and was short of 8 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?
| |
Riordan |
Julian |
| Number |
1 u |
1 u |
| Value |
6 |
9 |
| Total value |
6 u + 4 |
9 u - 8 |
The total number of candy canes that Riordan and Julian each had is the same.
9 u - 8 = 6 u + 4
9 u - 6 u = 8 + 4
3 u = 12
1 u = 12 ÷ 3 = 4
Number of packets that each had if they have used the same number of packets = 4
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24
Multiples of 6 (+4): 10, 16, 22, 28
Multiples of 9: 9, 18, 27, 36
Multiples of 9 (-8): 1, 10, 19, 28
Smallest common number: 28
Riordan needs 4 packets of 6 candy canes and Julian needs 3 packets of 9 candy canes.
Smallest possible number of candy canes each of them had if they used different number of packets = 28
Answer(s): (a) 4; (b) 28
