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Finding the Third Proportional to 102,419 and 213,013

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Solution

The third proportional to 102,419 and 213,013 is: 443,028.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,419 : 213,013 = 213,013 : x
  2. Step 2: Convert to fraction form
    102,419/213,013 = 213,013/x
  3. Step 3: Cross multiply
    102,419x = 213,013 × 213,013
  4. Step 4: Simplify right side
    102,419x = 45,374,538,169
  5. Step 5: Solve for x
    x = 45,374,538,169/102,419
  6. Step 6: Final answer
    x = 443,028.52

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.