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Finding the Third Proportional to 102,977 and 164,458

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Solution

The third proportional to 102,977 and 164,458 is: 262,645.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,977 : 164,458 = 164,458 : x
  2. Step 2: Convert to fraction form
    102,977/164,458 = 164,458/x
  3. Step 3: Cross multiply
    102,977x = 164,458 × 164,458
  4. Step 4: Simplify right side
    102,977x = 27,046,433,764
  5. Step 5: Solve for x
    x = 27,046,433,764/102,977
  6. Step 6: Final answer
    x = 262,645.38

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.