The Prevu Theater keeps a set of five counterweights to help stagehands move heavy props. The weights can balance exactly any load that is a multiple of 10 kg, from 10 kg up to a total of the five weights. Give the masses of weights which meet these conditions and allow the stagehands to counterbalance the maxium possible load.
see your other post. Then answer is hidden in the .5 gram answer.
I'm sorry, but I don't understand...
The answer is 10, 20, 40, 80, and 160.
To find the masses of the five counterweights, we need to determine the possible combinations that add up to the maximum load while having each load as a multiple of 10 kg. Let's start with the smallest multiple of 10 kg, which is 10 kg.
To achieve 10 kg, we need at least one counterweight. Let's consider the possible masses of the counterweights:
1. Counterweight 1: 10 kg
The maximum possible load obtainable with only 10 kg counterweight is 10 kg. However, we need to counterbalance a higher load, so we can explore other combinations.
2. Counterweight 1: 20 kg
Now, let's consider having a combination of two counterweights:
1. Counterweight 1: 10 kg
2. Counterweight 2: 10 kg
The maximum possible load is 20 kg (10 kg + 10 kg).
3. Counterweight 1: 20 kg
4. Counterweight 2: 10 kg
The maximum possible load is 30 kg (20 kg + 10 kg).
5. Counterweight 1: 20 kg
6. Counterweight 2: 20 kg
The maximum possible load is 40 kg (20 kg + 20 kg).
Now, let's see the combinations with three counterweights:
1. Counterweight 1: 10 kg
2. Counterweight 2: 10 kg
3. Counterweight 3: 10 kg
The maximum possible load is 30 kg (10 kg + 10 kg + 10 kg).
2. Counterweight 1: 20 kg
3. Counterweight 2: 10 kg
4. Counterweight 3: 10 kg
The maximum possible load is 40 kg (20 kg + 10 kg + 10 kg).
3. Counterweight 1: 20 kg
4. Counterweight 2: 20 kg
5. Counterweight 3: 10 kg
The maximum possible load is 50 kg (20 kg + 20 kg + 10 kg).
6. Counterweight 1: 20 kg
7. Counterweight 2: 20 kg
8. Counterweight 3: 20 kg
The maximum possible load is 60 kg (20 kg + 20 kg + 20 kg).
From the combinations above, we can determine the following masses for the five counterweights that allow the stagehands to counterbalance the maximum possible load:
- 20 kg (one counterweight)
- 10 kg (two counterweights)
- 20 kg (two counterweights)
- 10 kg (three counterweights)
- 20 kg (three counterweights)
Thus, the masses of the five counterweights are: 20 kg, 10 kg, 20 kg, 10 kg, and 20 kg.