Jack and Ken had the same number of sweets. Each of them packed his own sweets into packets. Jack packed 7 sweets in each packet and had 3 sweets left. Ken packed 10 sweets in each packet and was short of 6 sweets.

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 sweets each of them had if they used different number of packets? 

	Jack	Ken
Number	1 u	1 u
Value	7	10
Total value	7 u + 3	10 u - 6

The total number of sweets that Jack and Ken 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

Jack needs 3 packets of 7 sweets and Ken needs 2 packets of 10 sweets.

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


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