Howard and Lee had the same number of lollipops. Each of them packed his own lollipops into packets. Howard packed 6 lollipops in each packet and had 2 lollipops left. Lee packed 8 lollipops in each packet and was short of 2 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?
| |
Howard |
Lee |
| Number |
1 u |
1 u |
| Value |
6 |
8 |
| Total value |
6 u + 2 |
8 u - 2 |
The total number of lollipops that Howard and Lee each had is the same.
8 u - 2 = 6 u + 2
8 u - 6 u = 2 + 2
2 u = 4
1 u = 4 ÷ 2 = 2
Number of packets that each had if they have used the same number of packets = 2
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24, 30, 36
Multiples of 6 (+2): 8, 14, 20, 26, 32, 38
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 8 (-2): 6, 14, 22, 30, 38
Smallest common number: 38
Howard needs 6 packets of 6 lollipops and Lee needs 4 packets of 8 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 38
Answer(s): (a) 2; (b) 38
