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Finding the Third Proportional to 461,144 and 972,419

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Solution

The third proportional to 461,144 and 972,419 is: 2,050,549.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    461,144 : 972,419 = 972,419 : x
  2. Step 2: Convert to fraction form
    461,144/972,419 = 972,419/x
  3. Step 3: Cross multiply
    461,144x = 972,419 × 972,419
  4. Step 4: Simplify right side
    461,144x = 945,598,711,561
  5. Step 5: Solve for x
    x = 945,598,711,561/461,144
  6. Step 6: Final answer
    x = 2,050,549.74

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.