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Sagot :
To determine the weight of the fourth package, we follow these steps:
1. Calculate the total weight of all packages combined:
Given the mean (average) weight of the packages is 2.5 pounds and there are 4 packages, we first find the total weight of all the packages combined.
[tex]\[ \text{Total weight} = \text{Mean weight} \times \text{Number of packages} = 2.5 \times 4 = 10 \text{ pounds} \][/tex]
2. Sum the weights of the known packages:
We know the weights of three of the packages: 1.8 pounds, 3.2 pounds, and 2.7 pounds. We sum these weights to find the total weight of the known packages.
[tex]\[ \text{Sum of known weights} = 1.8 + 3.2 + 2.7 = 7.7 \text{ pounds} \][/tex]
3. Find the weight of the fourth package:
To find the weight of the fourth package, we subtract the sum of the weights of the known packages from the total weight of all packages combined.
[tex]\[ \text{Weight of the fourth package} = \text{Total weight} - \text{Sum of known weights} = 10 - 7.7 = 2.3 \text{ pounds} \][/tex]
4. Verify with the given options:
- 2.3
- 2.8
- 3.3
The weight of the fourth package is 2.3 pounds, which is one of the given options.
Thus, the weight of the fourth package is 2.3 pounds.
1. Calculate the total weight of all packages combined:
Given the mean (average) weight of the packages is 2.5 pounds and there are 4 packages, we first find the total weight of all the packages combined.
[tex]\[ \text{Total weight} = \text{Mean weight} \times \text{Number of packages} = 2.5 \times 4 = 10 \text{ pounds} \][/tex]
2. Sum the weights of the known packages:
We know the weights of three of the packages: 1.8 pounds, 3.2 pounds, and 2.7 pounds. We sum these weights to find the total weight of the known packages.
[tex]\[ \text{Sum of known weights} = 1.8 + 3.2 + 2.7 = 7.7 \text{ pounds} \][/tex]
3. Find the weight of the fourth package:
To find the weight of the fourth package, we subtract the sum of the weights of the known packages from the total weight of all packages combined.
[tex]\[ \text{Weight of the fourth package} = \text{Total weight} - \text{Sum of known weights} = 10 - 7.7 = 2.3 \text{ pounds} \][/tex]
4. Verify with the given options:
- 2.3
- 2.8
- 3.3
The weight of the fourth package is 2.3 pounds, which is one of the given options.
Thus, the weight of the fourth package is 2.3 pounds.
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