Gabriel and Bobby had the same number of lollipops. Each of them packed his own lollipops into packets. Gabriel packed 7 lollipops in each packet and had 4 lollipops left. Bobby packed 10 lollipops in each packet and was short of 5 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?
|
Gabriel |
Bobby |
Number |
1 u |
1 u |
Value |
7 |
10 |
Total value |
7 u + 4 |
10 u - 5 |
The total number of lollipops that Gabriel and Bobby each had is the same.
10 u - 5 = 7 u + 4
10 u - 7 u = 5 + 4
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 7: 7, 14, 21
Multiples of 7 (+4): 11, 18, 25
Multiples of 10: 10, 20, 30
Multiples of 10 (-5): 5, 15, 25
Smallest common number: 25
Gabriel needs 3 packets of 7 lollipops and Bobby needs 2 packets of 10 lollipops.
Smallest possible number of lollipops each of them had if they used different number of packets = 25
Answer(s): (a) 3; (b) 25