Gabriel and Warren had the same number of jelly beans. Each of them packed his own jelly beans into packets. Gabriel packed 8 jelly beans in each packet and had 4 jelly beans left. Warren packed 10 jelly beans in each packet and was short of 2 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?
| |
Gabriel |
Warren |
| Number |
1 u |
1 u |
| Value |
8 |
10 |
| Total value |
8 u + 4 |
10 u - 2 |
The total number of jelly beans that Gabriel and Warren each had is the same.
10 u - 2 = 8 u + 4
10 u - 8 u = 2 + 4
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 (+4): 12, 20, 28
Multiples of 10: 10, 20, 30
Multiples of 10 (-2): 8, 18, 28
Smallest common number: 28
Gabriel needs 3 packets of 8 jelly beans and Warren needs 2 packets of 10 jelly beans.
Smallest possible number of jelly beans each of them had if they used different number of packets = 28
Answer(s): (a) 3; (b) 28
