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Finding the Third Proportional to 461,716 and 698,709

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Solution

The third proportional to 461,716 and 698,709 is: 1,057,347.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    461,716 : 698,709 = 698,709 : x
  2. Step 2: Convert to fraction form
    461,716/698,709 = 698,709/x
  3. Step 3: Cross multiply
    461,716x = 698,709 × 698,709
  4. Step 4: Simplify right side
    461,716x = 488,194,266,681
  5. Step 5: Solve for x
    x = 488,194,266,681/461,716
  6. Step 6: Final answer
    x = 1,057,347.52

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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.