Rael and Pierre had the same number of chocolate bars. Each of them packed his own chocolate bars into packets. Rael packed 7 chocolate bars in each packet and had 3 chocolate bars left. Pierre packed 9 chocolate bars in each packet and was short of 3 chocolate bars.

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 chocolate bars each of them had if they used different number of packets? 

	Rael	Pierre
Number	1 u	1 u
Value	7	9
Total value	7 u + 3	9 u - 3

The total number of chocolate bars that Rael and Pierre each had is the same.

9 u - 3 = 7 u + 3
9 u - 7 u = 3 + 3
2 u = 6

1 u = 6 ÷ 2 = 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 9: 9, 18, 27
Multiples of 9 (-3): 6, 15, 24

Smallest common number: 24

Rael needs 3 packets of 7 chocolate bars and Pierre needs 2 packets of 9 chocolate bars.

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


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