Andy and Carl had the same number of lollipops. Each of them packed his own lollipops into packets. Andy packed 8 lollipops in each packet and had 2 lollipops left. Carl packed 10 lollipops in each packet and was short of 6 lollipops.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of lollipops each of them had if they used different number of packets?
|
Andy |
Carl |
Number |
1 u |
1 u |
Value |
8 |
10 |
Total value |
8 u + 2 |
10 u - 6 |
The total number of lollipops that Andy and Carl each had is the same.
10 u - 6 = 8 u + 2
10 u - 8 u = 6 + 2
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 (+2): 10, 18, 26, 34
Multiples of 10: 10, 20, 30, 40
Multiples of 10 (-6): 4, 14, 24, 34
Smallest common number: 34
Andy needs 4 packets of 8 lollipops and Carl needs 3 packets of 10 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 34
Answer(s): (a) 4; (b) 34