Zane and Ken had the same number of sweets. Each of them packed his own sweets into packets. Zane packed 7 sweets in each packet and had 5 sweets left. Ken packed 10 sweets in each packet and was short of 4 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?
|
Zane |
Ken |
Number |
1 u |
1 u |
Value |
7 |
10 |
Total value |
7 u + 5 |
10 u - 4 |
The total number of sweets that Zane and Ken each had is the same.
10 u - 4 = 7 u + 5
10 u - 7 u = 4 + 5
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 (+5): 12, 19, 26
Multiples of 10: 10, 20, 30
Multiples of 10 (-4): 6, 16, 26
Smallest common number: 26
Zane needs 3 packets of 7 sweets and Ken needs 2 packets of 10 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 26
Answer(s): (a) 3; (b) 26