Reggie and Will had the same number of candy canes. Each of them packed his own candy canes into packets. Reggie packed 6 candy canes in each packet and had 3 candy canes left. Will packed 8 candy canes in each packet and was short of 7 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?
|
Reggie |
Will |
Number |
1 u |
1 u |
Value |
6 |
8 |
Total value |
6 u + 3 |
8 u - 7 |
The total number of candy canes that Reggie and Will each had is the same.
8 u - 7 = 6 u + 3
8 u - 6 u = 7 + 3
2 u = 10
1 u = 10 ÷ 2 = 5
Number of packets that each had if they have used the same number of packets = 5
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 6 (+3): 9, 15, 21, 27, 33
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 8 (-7): 1, 9, 17, 25, 33
Smallest common number: 33
Reggie needs 5 packets of 6 candy canes and Will needs 4 packets of 8 candy canes.
Smallest possible number of candy canes each of them had if they used different number of packets = 33
Answer(s): (a) 5; (b) 33