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Finding the Third Proportional to 408,078 and 643,419

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Solution

The third proportional to 408,078 and 643,419 is: 1,014,482.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    408,078 : 643,419 = 643,419 : x
  2. Step 2: Convert to fraction form
    408,078/643,419 = 643,419/x
  3. Step 3: Cross multiply
    408,078x = 643,419 × 643,419
  4. Step 4: Simplify right side
    408,078x = 413,988,009,561
  5. Step 5: Solve for x
    x = 413,988,009,561/408,078
  6. Step 6: Final answer
    x = 1,014,482.55

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.