Oliver and Michael had the same number of lollipops. Each of them packed his own lollipops into packets. Oliver packed 6 lollipops in each packet and had 4 lollipops left. Michael packed 10 lollipops in each packet and was short of 8 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?
| |
Oliver |
Michael |
| Number |
1 u |
1 u |
| Value |
6 |
10 |
| Total value |
6 u + 4 |
10 u - 8 |
The total number of lollipops that Oliver and Michael each had is the same.
10 u - 8 = 6 u + 4
10 u - 6 u = 8 + 4
4 u = 12
1 u = 12 ÷ 4 = 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
Multiples of 6 (+4): 10, 16, 22
Multiples of 10: 10, 20, 30
Multiples of 10 (-8): 2, 12, 22
Smallest common number: 22
Oliver needs 3 packets of 6 lollipops and Michael needs 2 packets of 10 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 22
Answer(s): (a) 3; (b) 22
