Michael and Lee had the same number of chocolate bars. Each of them packed his own chocolate bars into packets. Michael packed 8 chocolate bars in each packet and had 3 chocolate bars left. Lee packed 11 chocolate bars in each packet and was short of 9 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?
|
Michael |
Lee |
Number |
1 u |
1 u |
Value |
8 |
11 |
Total value |
8 u + 3 |
11 u - 9 |
The total number of chocolate bars that Michael and Lee each had is the same.
11 u - 9 = 8 u + 3
11 u - 8 u = 9 + 3
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 8: 8, 16, 24, 32
Multiples of 8 (+3): 11, 19, 27, 35
Multiples of 11: 11, 22, 33, 44
Multiples of 11 (-9): 2, 13, 24, 35
Smallest common number: 35
Michael needs 4 packets of 8 chocolate bars and Lee needs 3 packets of 11 chocolate bars.
Smallest possible number of chocolate bars each of them had if they used different number of packets = 35
Answer(s): (a) 4; (b) 35