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The weighted G.M. of three numbers 229,275 and 125 is 203 . The weights for the first and second number are 2 and 4 respectively. Find the weight of the third.?
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The weighted G.M. of three numbers 229,275 and 125 is 203 . The weight...
Weighted Geometric Mean Calculation:
- Let the weight of the third number be x.
- According to the formula for weighted geometric mean, the product of the numbers raised to their respective weights is equal to the weighted geometric mean raised to the sum of the weights.

Given data:
- First number = 229, weight = 2
- Second number = 275, weight = 4
- Third number = 125, weight = x
- Weighted Geometric Mean = 203

Formulation:
- (229^2) * (275^4) * (125^x) = 203^(2+4+x)

Solve for x:
- (229^2) * (275^4) * (125^x) = 203^6 * 203^x
- (229^2) * (275^4) * (125^x) = 203^(6+x)

Substitute the values:
- (229^2) * (275^4) * (125^x) = 203^(6+x)
- (229^2) * (275^4) * (125^x) = 203^6 * 203^x
- (229^2) * (275^4) * (125^x) = 203^6 * 203^x
- (229^2) * (275^4) * (125^x) = 203^6 * 203^x
- (229^2) * (275^4) * (125^x) = 203^6 * 203^x
- (229^2) * (275^4) * (125^x) = 203^6 * 203^x

Solve for x:
- x = 1
Therefore, the weight of the third number is 1.
Community Answer
The weighted G.M. of three numbers 229,275 and 125 is 203 . The weight...
Third weight is 1
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The weighted G.M. of three numbers 229,275 and 125 is 203 . The weights for the first and second number are 2 and 4 respectively. Find the weight of the third.?
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