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Finding the Third Proportional to 307,814 and 463,749

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Solution

The third proportional to 307,814 and 463,749 is: 698,678.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    307,814 : 463,749 = 463,749 : x
  2. Step 2: Convert to fraction form
    307,814/463,749 = 463,749/x
  3. Step 3: Cross multiply
    307,814x = 463,749 × 463,749
  4. Step 4: Simplify right side
    307,814x = 215,063,135,001
  5. Step 5: Solve for x
    x = 215,063,135,001/307,814
  6. Step 6: Final answer
    x = 698,678.86

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.