Vincent and Warren had the same number of sweets. Each of them packed his own sweets into packets. Vincent packed 6 sweets in each packet and had 2 sweets left. Warren packed 10 sweets in each packet and was short of 6 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?
| |
Vincent |
Warren |
| Number |
1 u |
1 u |
| Value |
6 |
10 |
| Total value |
6 u + 2 |
10 u - 6 |
The total number of sweets that Vincent and Warren each had is the same.
10 u - 6 = 6 u + 2
10 u - 6 u = 6 + 2
4 u = 8
1 u = 8 ÷ 4 = 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, 36, 42
Multiples of 6 (+2): 8, 14, 20, 26, 32, 38, 44
Multiples of 10: 10, 20, 30, 40, 50
Multiples of 10 (-6): 4, 14, 24, 34, 44
Smallest common number: 44
Vincent needs 7 packets of 6 sweets and Warren needs 4 packets of 10 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 44
Answer(s): (a) 2; (b) 44
