Charlie and George had the same number of jelly beans. Each of them packed his own jelly beans into packets. Charlie packed 6 jelly beans in each packet and had 5 jelly beans left. George packed 8 jelly beans in each packet and was short of 3 jelly beans.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of jelly beans each of them had if they used different number of packets?
|
Charlie |
George |
Number |
1 u |
1 u |
Value |
6 |
8 |
Total value |
6 u + 5 |
8 u - 3 |
The total number of jelly beans that Charlie and George each had is the same.
8 u - 3 = 6 u + 5
8 u - 6 u = 3 + 5
2 u = 8
1 u = 8 ÷ 2 = 4
Number of packets that each had if they have used the same number of packets = 4
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24
Multiples of 6 (+5): 11, 17, 23, 29
Multiples of 8: 8, 16, 24, 32
Multiples of 8 (-3): 5, 13, 21, 29
Smallest common number: 29
Charlie needs 4 packets of 6 jelly beans and George needs 3 packets of 8 jelly beans.
Smallest possible number of jelly beans each of them had if they used different number of packets = 29
Answer(s): (a) 4; (b) 29