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Finding the Third Proportional to 205,121 and 430,971

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Solution

The third proportional to 205,121 and 430,971 is: 905,494.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,121 : 430,971 = 430,971 : x
  2. Step 2: Convert to fraction form
    205,121/430,971 = 430,971/x
  3. Step 3: Cross multiply
    205,121x = 430,971 × 430,971
  4. Step 4: Simplify right side
    205,121x = 185,736,002,841
  5. Step 5: Solve for x
    x = 185,736,002,841/205,121
  6. Step 6: Final answer
    x = 905,494.82

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.