Tommy and Fabian had the same number of sweets. Each of them packed his own sweets into packets. Tommy packed 6 sweets in each packet and had 2 sweets left. Fabian packed 9 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?
| |
Tommy |
Fabian |
| Number |
1 u |
1 u |
| Value |
6 |
9 |
| Total value |
6 u + 2 |
9 u - 7 |
The total number of sweets that Tommy and Fabian each had is the same.
9 u - 7 = 6 u + 2
9 u - 6 u = 7 + 2
3 u = 9
1 u = 9 ÷ 3 = 3
Number of packets that each had if they have used the same number of packets = 3
(b)
The number of packets that each had is different.
Multiples of 6: 6, 12, 18, 24, 30, 36
Multiples of 6 (+2): 8, 14, 20, 26, 32, 38
Multiples of 9: 9, 18, 27, 36, 45
Multiples of 9 (-7): 2, 11, 20, 29, 38
Smallest common number: 38
Tommy needs 6 packets of 6 sweets and Fabian needs 4 packets of 9 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 38
Answer(s): (a) 3; (b) 38
