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Finding the Third Proportional to 386,817 and 823,459

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Solution

The third proportional to 386,817 and 823,459 is: 1,752,985.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    386,817 : 823,459 = 823,459 : x
  2. Step 2: Convert to fraction form
    386,817/823,459 = 823,459/x
  3. Step 3: Cross multiply
    386,817x = 823,459 × 823,459
  4. Step 4: Simplify right side
    386,817x = 678,084,724,681
  5. Step 5: Solve for x
    x = 678,084,724,681/386,817
  6. Step 6: Final answer
    x = 1,752,985.84

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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.