Pierre and Sam had the same number of sweets. Each of them packed his own sweets into packets. Pierre packed 8 sweets in each packet and had 7 sweets left. Sam packed 12 sweets in each packet and was short of 9 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?
| |
Pierre |
Sam |
| Number |
1 u |
1 u |
| Value |
8 |
12 |
| Total value |
8 u + 7 |
12 u - 9 |
The total number of sweets that Pierre and Sam each had is the same.
12 u - 9 = 8 u + 7
12 u - 8 u = 9 + 7
4 u = 16
1 u = 16 ÷ 4 = 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 (+7): 15, 23, 31, 39
Multiples of 12: 12, 24, 36, 48
Multiples of 12 (-9): 3, 15, 27, 39
Smallest common number: 39
Pierre needs 4 packets of 8 sweets and Sam needs 3 packets of 12 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 39
Answer(s): (a) 4; (b) 39
