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Finding the Third Proportional to 471,564 and 964,916

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Solution

The third proportional to 471,564 and 964,916 is: 1,974,414.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    471,564 : 964,916 = 964,916 : x
  2. Step 2: Convert to fraction form
    471,564/964,916 = 964,916/x
  3. Step 3: Cross multiply
    471,564x = 964,916 × 964,916
  4. Step 4: Simplify right side
    471,564x = 931,062,887,056
  5. Step 5: Solve for x
    x = 931,062,887,056/471,564
  6. Step 6: Final answer
    x = 1,974,414.69

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.