Charlie and Daniel had the same number of jelly beans. Each of them packed his own jelly beans into packets. Charlie packed 8 jelly beans in each packet and had 2 jelly beans left. Daniel packed 10 jelly beans in each packet and was short of 4 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 |
Daniel |
| Number |
1 u |
1 u |
| Value |
8 |
10 |
| Total value |
8 u + 2 |
10 u - 4 |
The total number of jelly beans that Charlie and Daniel each had is the same.
10 u - 4 = 8 u + 2
10 u - 8 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 8: 8, 16, 24
Multiples of 8 (+2): 10, 18, 26
Multiples of 10: 10, 20, 30
Multiples of 10 (-4): 6, 16, 26
Smallest common number: 26
Charlie needs 3 packets of 8 jelly beans and Daniel needs 2 packets of 10 jelly beans.
Smallest possible number of jelly beans each of them had if they used different number of packets = 26
Answer(s): (a) 3; (b) 26
