A salesperson learned that the town\'s butcher needed to buy a scale to weigh me
ID: 3565890 • Letter: A
Question
A salesperson learned that the town's butcher needed to buy a scale to weigh meats from 1 to 40 pounds. The salesperson convinced the butcher that he could save him a lot of money. He would sell the butcher the double pan beam balance and the 4 weights below at a big discount and that it would fully satisfy the butcher's needs.
The butcher bought the scale and weights. Did he get taken? Is it really possible to weigh all integer increments from 1-40 using only 4 weights? Justify your answer.
A salesperson learned that the town's butcher needed to buy a scale to weigh meats from 1 to 40 pounds. The salesperson convinced the butcher that he could save him a lot of money. He would sell the butcher the double pan beam balance and the 4 weights below at a big discount and that it would fully satisfy the butcher's needs. The butcher bought the scale and weights. Did he get taken? Is it really possible to weigh all integer increments from 1-40 using only 4 weights? Justify your answer.Explanation / Answer
Yes it is possible to weigh all integers increment from 1 to 40 using four numbers.
The numbers are 1, 3, 9, 27.
Explanation:
2 = 3 - 1
4 = 3 + 1
5 = 9 - 3 - 1
6 = 9 - 3
7 = 9 + 1 - 3
8 = 9 - 1
10 = 9 + 1
11 = 9 + 3 - 1
12 = 9 + 3
13 = 9 + 3 + 1
14 = 27 - 9 - 3 - 1
15 = 27 - 9 - 3
16 = 27 + 1 - 9 - 3
17 = 27 - 9 - 1
18 = 27 - 9
19 = 27 - 9 + 1
20 = 27 + 3 - 9 - 1
21 = 27 + 3 - 9 + 1
22 = 27 - 9 + 3 + 1
23 = 27 - 3 - 1
24 = 27 - 3
25 = 27 - 3 + 1
26 = 27 - 1
28 = 27 + 1
29 = 27 - 1 + 3
30 = 27 + 3
31 = 27 + 1 + 3
32 = 27 - 1 - 3 + 9
33 = 27 - 3 + 9
34 = 27 - 3 + 1 + 9
35 = 27 - 1 + 9
36 = 27 + 9
37 = 27 + 9 + 1
38 = 27 + 9 + 3 - 1
39 = 27 + 9 + 3
40 = 27 + 9 + 3 + 1
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