Andy and Caden had the same number of chocolate bars. Each of them packed his own chocolate bars into packets. Andy packed 6 chocolate bars in each packet and had 5 chocolate bars left. Caden packed 9 chocolate bars in each packet and was short of 7 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?
|
Andy |
Caden |
Number |
1 u |
1 u |
Value |
6 |
9 |
Total value |
6 u + 5 |
9 u - 7 |
The total number of chocolate bars that Andy and Caden each had is the same.
9 u - 7 = 6 u + 5
9 u - 6 u = 7 + 5
3 u = 12
1 u = 12 ÷ 3 = 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 (+5): 11, 17, 23, 29
Multiples of 9: 9, 18, 27, 36
Multiples of 9 (-7): 2, 11, 20, 29
Smallest common number: 29
Andy needs 4 packets of 6 chocolate bars and Caden needs 3 packets of 9 chocolate bars.
Smallest possible number of chocolate bars each of them had if they used different number of packets = 29
Answer(s): (a) 4; (b) 29