Tommy and Simon had the same number of candy canes. Each of them packed his own candy canes into packets. Tommy packed 8 candy canes in each packet and had 5 candy canes left. Simon packed 10 candy canes in each packet and was short of 3 candy canes.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of candy canes each of them had if they used different number of packets?
|
Tommy |
Simon |
Number |
1 u |
1 u |
Value |
8 |
10 |
Total value |
8 u + 5 |
10 u - 3 |
The total number of candy canes that Tommy and Simon each had is the same.
10 u - 3 = 8 u + 5
10 u - 8 u = 3 + 5
2 u = 8
1 u = 8 ÷ 2 = 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 (+5): 13, 21, 29, 37
Multiples of 10: 10, 20, 30, 40
Multiples of 10 (-3): 7, 17, 27, 37
Smallest common number: 37
Tommy needs 4 packets of 8 candy canes and Simon needs 3 packets of 10 candy canes.
Smallest possible number of candy canes each of them had if they used different number of packets = 37
Answer(s): (a) 4; (b) 37