Zeph and Ian had the same number of jelly beans. Each of them packed his own jelly beans into packets. Zeph packed 7 jelly beans in each packet and had 4 jelly beans left. Ian packed 11 jelly beans in each packet and was short of 8 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?
|
Zeph |
Ian |
Number |
1 u |
1 u |
Value |
7 |
11 |
Total value |
7 u + 4 |
11 u - 8 |
The total number of jelly beans that Zeph and Ian each had is the same.
11 u - 8 = 7 u + 4
11 u - 7 u = 8 + 4
4 u = 12
1 u = 12 ÷ 4 = 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 7: 7, 14, 21
Multiples of 7 (+4): 11, 18, 25
Multiples of 11: 11, 22, 33
Multiples of 11 (-8): 3, 14, 25
Smallest common number: 25
Zeph needs 3 packets of 7 jelly beans and Ian needs 2 packets of 11 jelly beans.
Smallest possible number of jelly beans each of them had if they used different number of packets = 25
Answer(s): (a) 3; (b) 25