John and Ian had the same number of jelly beans. Each of them packed his own jelly beans into packets. John packed 6 jelly beans in each packet and had 3 jelly beans left. Ian packed 9 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?
| |
John |
Ian |
| Number |
1 u |
1 u |
| Value |
6 |
9 |
| Total value |
6 u + 3 |
9 u - 3 |
The total number of jelly beans that John and Ian each had is the same.
9 u - 3 = 6 u + 3
9 u - 6 u = 3 + 3
3 u = 6
1 u = 6 ÷ 3 = 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 6: 6, 12, 18, 24, 30
Multiples of 6 (+3): 9, 15, 21, 27, 33
Multiples of 9: 9, 18, 27, 36
Multiples of 9 (-3): 6, 15, 24, 33
Smallest common number: 33
John needs 5 packets of 6 jelly beans and Ian needs 3 packets of 9 jelly beans.
Smallest possible number of jelly beans each of them had if they used different number of packets = 33
Answer(s): (a) 2; (b) 33
