Cody and Vincent had the same number of chocolate bars. Each of them packed his own chocolate bars into packets. Cody packed 6 chocolate bars in each packet and had 2 chocolate bars left. Vincent packed 8 chocolate bars in each packet and was short of 6 chocolate bars.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of chocolate bars each of them had if they used different number of packets?
| |
Cody |
Vincent |
| Number |
1 u |
1 u |
| Value |
6 |
8 |
| Total value |
6 u + 2 |
8 u - 6 |
The total number of chocolate bars that Cody and Vincent each had is the same.
8 u - 6 = 6 u + 2
8 u - 6 u = 6 + 2
2 u = 8
1 u = 8 ÷ 2 = 4
Number of packets that each had if they have used the same number of packets = 4
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24
Multiples of 6 (+2): 8, 14, 20, 26
Multiples of 8: 8, 16, 24, 32
Multiples of 8 (-6): 2, 10, 18, 26
Smallest common number: 26
Cody needs 4 packets of 6 chocolate bars and Vincent needs 3 packets of 8 chocolate bars.
Smallest possible number of chocolate bars each of them had if they used different number of packets = 26
Answer(s): (a) 4; (b) 26
