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Finding the Third Proportional to 412,206 and 878,412

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Solution

The third proportional to 412,206 and 878,412 is: 1,871,898.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,206 : 878,412 = 878,412 : x
  2. Step 2: Convert to fraction form
    412,206/878,412 = 878,412/x
  3. Step 3: Cross multiply
    412,206x = 878,412 × 878,412
  4. Step 4: Simplify right side
    412,206x = 771,607,641,744
  5. Step 5: Solve for x
    x = 771,607,641,744/412,206
  6. Step 6: Final answer
    x = 1,871,898.13

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.