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Finding the Third Proportional to 133,585 and 213,013

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Solution

The third proportional to 133,585 and 213,013 is: 339,667.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    133,585 : 213,013 = 213,013 : x
  2. Step 2: Convert to fraction form
    133,585/213,013 = 213,013/x
  3. Step 3: Cross multiply
    133,585x = 213,013 × 213,013
  4. Step 4: Simplify right side
    133,585x = 45,374,538,169
  5. Step 5: Solve for x
    x = 45,374,538,169/133,585
  6. Step 6: Final answer
    x = 339,667.91

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.