Tom and Fabian had the same number of lollipops. Each of them packed his own lollipops into packets. Tom packed 8 lollipops in each packet and had 4 lollipops left. Fabian packed 10 lollipops in each packet and was short of 4 lollipops.

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

	Tom	Fabian
Number	1 u	1 u
Value	8	10
Total value	8 u + 4	10 u - 4

The total number of lollipops that Tom and Fabian each had is the same.

10 u - 4 = 8 u + 4
10 u - 8 u = 4 + 4
2 u = 8

1 u = 8 ÷ 2 = 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 8: 8, 16, 24, 32
Multiples of 8 (+4): 12, 20, 28, 36 

Multiples of 10: 10, 20, 30, 40
Multiples of 10 (-4): 6, 16, 26, 36

Smallest common number: 36

Tom needs 4 packets of 8 lollipops and Fabian needs 3 packets of 10 lollipops.

Smallest possible number of lollipops each of them had if they used different number of packets = 36


Answer(s): (a) 4; (b) 36