Albert and David had the same number of candy canes. Each of them packed his own candy canes into packets. Albert packed 7 candy canes in each packet and had 3 candy canes left. David packed 10 candy canes in each packet and was short of 6 candy canes.

1. How many packets did each of them have if they have used the same number of packets?
2. What was the smallest possible number of candy canes each of them had if they used different number of packets? 

	Albert	David
Number	1 u	1 u
Value	7	10
Total value	7 u + 3	10 u - 6

The total number of candy canes that Albert and David each had is the same.

10 u - 6 = 7 u + 3
10 u - 7 u = 6 + 3
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 7: 7, 14, 21
Multiples of 7 (+3): 10, 17, 24 

Multiples of 10: 10, 20, 30
Multiples of 10 (-6): 4, 14, 24

Smallest common number: 24

Albert needs 3 packets of 7 candy canes and David needs 2 packets of 10 candy canes.

Smallest possible number of candy canes each of them had if they used different number of packets = 24


Answer(s): (a) 3; (b) 24