Fred and Warren had the same number of lollipops. Each of them packed his own lollipops into packets. Fred packed 6 lollipops in each packet and had 3 lollipops left. Warren packed 8 lollipops in each packet and was short of 3 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?
|
Fred |
Warren |
Number |
1 u |
1 u |
Value |
6 |
8 |
Total value |
6 u + 3 |
8 u - 3 |
The total number of lollipops that Fred and Warren each had is the same.
8 u - 3 = 6 u + 3
8 u - 6 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 6: 6, 12, 18, 24, 30, 36, 42
Multiples of 6 (+3): 9, 15, 21, 27, 33, 39, 45
Multiples of 8: 8, 16, 24, 32, 40, 48
Multiples of 8 (-3): 5, 13, 21, 29, 37, 45
Smallest common number: 45
Fred needs 7 packets of 6 lollipops and Warren needs 5 packets of 8 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 45
Answer(s): (a) 3; (b) 45