Lee and Andy had the same number of chocolate bars. Each of them packed his own chocolate bars into packets. Lee packed 7 chocolate bars in each packet and had 4 chocolate bars left. Andy packed 9 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?
|
Lee |
Andy |
Number |
1 u |
1 u |
Value |
7 |
9 |
Total value |
7 u + 4 |
9 u - 6 |
The total number of chocolate bars that Lee and Andy each had is the same.
9 u - 6 = 7 u + 4
9 u - 7 u = 6 + 4
2 u = 10
1 u = 10 ÷ 2 = 5
Number of packets that each had if they have used the same number of packets = 5
(b)
The number of packets that each had is different.
Multiples of 7: 7, 14, 21, 28, 35
Multiples of 7 (+4): 11, 18, 25, 32, 39
Multiples of 9: 9, 18, 27, 36, 45
Multiples of 9 (-6): 3, 12, 21, 30, 39
Smallest common number: 39
Lee needs 5 packets of 7 chocolate bars and Andy needs 4 packets of 9 chocolate bars.
Smallest possible number of chocolate bars each of them had if they used different number of packets = 39
Answer(s): (a) 5; (b) 39