Ivan and Xavier had the same number of sweets. Each of them packed his own sweets into packets. Ivan packed 8 sweets in each packet and had 3 sweets left. Xavier packed 10 sweets in each packet and was short of 3 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?
| |
Ivan |
Xavier |
| Number |
1 u |
1 u |
| Value |
8 |
10 |
| Total value |
8 u + 3 |
10 u - 3 |
The total number of sweets that Ivan and Xavier each had is the same.
10 u - 3 = 8 u + 3
10 u - 8 u = 3 + 3
2 u = 6
1 u = 6 ÷ 2 = 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 8: 8, 16, 24
Multiples of 8 (+3): 11, 19, 27
Multiples of 10: 10, 20, 30
Multiples of 10 (-3): 7, 17, 27
Smallest common number: 27
Ivan needs 3 packets of 8 sweets and Xavier needs 2 packets of 10 sweets.
Smallest possible number of sweets each of them had if they used different number of packets = 27
Answer(s): (a) 3; (b) 27
