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Finding the Third Proportional to 262,638 and 407,457

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Solution

The third proportional to 262,638 and 407,457 is: 632,129.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,638 : 407,457 = 407,457 : x
  2. Step 2: Convert to fraction form
    262,638/407,457 = 407,457/x
  3. Step 3: Cross multiply
    262,638x = 407,457 × 407,457
  4. Step 4: Simplify right side
    262,638x = 166,021,206,849
  5. Step 5: Solve for x
    x = 166,021,206,849/262,638
  6. Step 6: Final answer
    x = 632,129.42

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.