Bobby and Justin had the same number of sweets. Each of them packed his own sweets into packets. Bobby packed 6 sweets in each packet and had 4 sweets left. Justin packed 9 sweets in each packet and was short of 5 sweets.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of sweets each of them had if they used different number of packets?
| |
Bobby |
Justin |
| Number |
1 u |
1 u |
| Value |
6 |
9 |
| Total value |
6 u + 4 |
9 u - 5 |
The total number of sweets that Bobby and Justin each had is the same.
9 u - 5 = 6 u + 4
9 u - 6 u = 5 + 4
3 u = 9
1 u = 9 ÷ 3 = 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 6: 6, 12, 18, 24, 30, 36
Multiples of 6 (+4): 10, 16, 22, 28, 34, 40
Multiples of 9: 9, 18, 27, 36, 45
Multiples of 9 (-5): 4, 13, 22, 31, 40
Smallest common number: 40
Bobby needs 6 packets of 6 sweets and Justin needs 4 packets of 9 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 40
Answer(s): (a) 3; (b) 40
