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Finding the Third Proportional to 415,464 and 678,348

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Solution

The third proportional to 415,464 and 678,348 is: 1,107,571.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    415,464 : 678,348 = 678,348 : x
  2. Step 2: Convert to fraction form
    415,464/678,348 = 678,348/x
  3. Step 3: Cross multiply
    415,464x = 678,348 × 678,348
  4. Step 4: Simplify right side
    415,464x = 460,156,009,104
  5. Step 5: Solve for x
    x = 460,156,009,104/415,464
  6. Step 6: Final answer
    x = 1,107,571.32

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.