Tom and Valen had the same number of sweets. Each of them packed his own sweets into packets. Tom packed 6 sweets in each packet and had 3 sweets left. Valen packed 9 sweets in each packet and was short of 3 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?
| |
Tom |
Valen |
| Number |
1 u |
1 u |
| Value |
6 |
9 |
| Total value |
6 u + 3 |
9 u - 3 |
The total number of sweets that Tom and Valen each had is the same.
9 u - 3 = 6 u + 3
9 u - 6 u = 3 + 3
3 u = 6
1 u = 6 ÷ 3 = 2
Number of packets that each had if they have used the same number of packets = 2
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 6 (+3): 9, 15, 21, 27, 33
Multiples of 9: 9, 18, 27, 36
Multiples of 9 (-3): 6, 15, 24, 33
Smallest common number: 33
Tom needs 5 packets of 6 sweets and Valen needs 3 packets of 9 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 33
Answer(s): (a) 2; (b) 33
