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Finding the Third Proportional to 380,780 and 827,209

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Solution

The third proportional to 380,780 and 827,209 is: 1,797,034.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    380,780 : 827,209 = 827,209 : x
  2. Step 2: Convert to fraction form
    380,780/827,209 = 827,209/x
  3. Step 3: Cross multiply
    380,780x = 827,209 × 827,209
  4. Step 4: Simplify right side
    380,780x = 684,274,729,681
  5. Step 5: Solve for x
    x = 684,274,729,681/380,780
  6. Step 6: Final answer
    x = 1,797,034.32

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.