Billy and Simon had the same number of sweets. Each of them packed his own sweets into packets. Billy packed 6 sweets in each packet and had 5 sweets left. Simon packed 8 sweets in each packet and was short of 7 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?
| |
Billy |
Simon |
| Number |
1 u |
1 u |
| Value |
6 |
8 |
| Total value |
6 u + 5 |
8 u - 7 |
The total number of sweets that Billy and Simon each had is the same.
8 u - 7 = 6 u + 5
8 u - 6 u = 7 + 5
2 u = 12
1 u = 12 ÷ 2 = 6
Number of packets that each had if they have used the same number of packets = 6
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24, 30, 36
Multiples of 6 (+5): 11, 17, 23, 29, 35, 41
Multiples of 8: 8, 16, 24, 32, 40, 48
Multiples of 8 (-7): 1, 9, 17, 25, 33, 41
Smallest common number: 41
Billy needs 6 packets of 6 sweets and Simon needs 5 packets of 8 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 41
Answer(s): (a) 6; (b) 41
