Henry and Oscar had the same number of jelly beans. Each of them packed his own jelly beans into packets. Henry packed 8 jelly beans in each packet and had 7 jelly beans left. Oscar packed 11 jelly beans in each packet and was short of 5 jelly beans.
- How many packets did each of them have if they have used the same number of packets?
- What was the smallest possible number of jelly beans each of them had if they used different number of packets?
|
Henry |
Oscar |
Number |
1 u |
1 u |
Value |
8 |
11 |
Total value |
8 u + 7 |
11 u - 5 |
The total number of jelly beans that Henry and Oscar each had is the same.
11 u - 5 = 8 u + 7
11 u - 8 u = 5 + 7
3 u = 12
1 u = 12 ÷ 3 = 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 (+7): 15, 23, 31, 39
Multiples of 11: 11, 22, 33, 44
Multiples of 11 (-5): 6, 17, 28, 39
Smallest common number: 39
Henry needs 4 packets of 8 jelly beans and Oscar needs 3 packets of 11 jelly beans.
Smallest possible number of jelly beans each of them had if they used different number of packets = 39
Answer(s): (a) 4; (b) 39