Flynn and Warren had the same number of lollipops. Each of them packed his own lollipops into packets. Flynn packed 8 lollipops in each packet and had 3 lollipops left. Warren packed 12 lollipops in each packet and was short of 5 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?
| |
Flynn |
Warren |
| Number |
1 u |
1 u |
| Value |
8 |
12 |
| Total value |
8 u + 3 |
12 u - 5 |
The total number of lollipops that Flynn and Warren each had is the same.
12 u - 5 = 8 u + 3
12 u - 8 u = 5 + 3
4 u = 8
1 u = 8 ÷ 4 = 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 8: 8, 16, 24, 32, 40
Multiples of 8 (+3): 11, 19, 27, 35, 43
Multiples of 12: 12, 24, 36, 48
Multiples of 12 (-5): 7, 19, 31, 43
Smallest common number: 43
Flynn needs 5 packets of 8 lollipops and Warren needs 3 packets of 12 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 43
Answer(s): (a) 2; (b) 43
