George and Daniel had the same number of lollipops. Each of them packed his own lollipops into packets. George packed 6 lollipops in each packet and had 2 lollipops left. Daniel packed 8 lollipops in each packet and was short of 4 lollipops.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of lollipops each of them had if they used different number of packets?
| |
George |
Daniel |
| Number |
1 u |
1 u |
| Value |
6 |
8 |
| Total value |
6 u + 2 |
8 u - 4 |
The total number of lollipops that George and Daniel each had is the same.
8 u - 4 = 6 u + 2
8 u - 6 u = 4 + 2
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 6: 6, 12, 18, 24, 30, 36, 42
Multiples of 6 (+2): 8, 14, 20, 26, 32, 38, 44
Multiples of 8: 8, 16, 24, 32, 40, 48
Multiples of 8 (-4): 4, 12, 20, 28, 36, 44
Smallest common number: 44
George needs 7 packets of 6 lollipops and Daniel needs 5 packets of 8 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 44
Answer(s): (a) 3; (b) 44
