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Finding the Third Proportional to 415,057 and 641,014

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Solution

The third proportional to 415,057 and 641,014 is: 989,981.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    415,057 : 641,014 = 641,014 : x
  2. Step 2: Convert to fraction form
    415,057/641,014 = 641,014/x
  3. Step 3: Cross multiply
    415,057x = 641,014 × 641,014
  4. Step 4: Simplify right side
    415,057x = 410,898,948,196
  5. Step 5: Solve for x
    x = 410,898,948,196/415,057
  6. Step 6: Final answer
    x = 989,981.97

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.