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Finding the Third Proportional to 262,401 and 417,735

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Solution

The third proportional to 262,401 and 417,735 is: 665,022.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,401 : 417,735 = 417,735 : x
  2. Step 2: Convert to fraction form
    262,401/417,735 = 417,735/x
  3. Step 3: Cross multiply
    262,401x = 417,735 × 417,735
  4. Step 4: Simplify right side
    262,401x = 174,502,530,225
  5. Step 5: Solve for x
    x = 174,502,530,225/262,401
  6. Step 6: Final answer
    x = 665,022.35

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.