Ben and Valen had the same number of lollipops. Each of them packed his own lollipops into packets. Ben packed 5 lollipops in each packet and had 4 lollipops left. Valen packed 7 lollipops in each packet and was short of 2 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? 

	Ben	Valen
Number	1 u	1 u
Value	5	7
Total value	5 u + 4	7 u - 2

The total number of lollipops that Ben and Valen each had is the same.

7 u - 2 = 5 u + 4
7 u - 5 u = 2 + 4
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 5: 5, 10, 15
Multiples of 5 (+4): 9, 14, 19 

Multiples of 7: 7, 14, 21
Multiples of 7 (-2): 5, 12, 19

Smallest common number: 19

Ben needs 3 packets of 5 lollipops and Valen needs 2 packets of 7 lollipops.

Smallest possible number of lollipops each of them had if they used different number of packets = 19


Answer(s): (a) 3; (b) 19