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Finding the Third Proportional to 321,357 and 657,456

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Solution

The third proportional to 321,357 and 657,456 is: 1,345,072.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    321,357 : 657,456 = 657,456 : x
  2. Step 2: Convert to fraction form
    321,357/657,456 = 657,456/x
  3. Step 3: Cross multiply
    321,357x = 657,456 × 657,456
  4. Step 4: Simplify right side
    321,357x = 432,248,391,936
  5. Step 5: Solve for x
    x = 432,248,391,936/321,357
  6. Step 6: Final answer
    x = 1,345,072.28

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.