Riordan and Mark had the same number of sweets. Each of them packed his own sweets into packets. Riordan packed 8 sweets in each packet and had 7 sweets left. Mark packed 11 sweets in each packet and was short of 2 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?
| |
Riordan |
Mark |
| Number |
1 u |
1 u |
| Value |
8 |
11 |
| Total value |
8 u + 7 |
11 u - 2 |
The total number of sweets that Riordan and Mark each had is the same.
11 u - 2 = 8 u + 7
11 u - 8 u = 2 + 7
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 8: 8, 16, 24
Multiples of 8 (+7): 15, 23, 31
Multiples of 11: 11, 22, 33
Multiples of 11 (-2): 9, 20, 31
Smallest common number: 31
Riordan needs 3 packets of 8 sweets and Mark needs 2 packets of 11 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 31
Answer(s): (a) 3; (b) 31
