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Finding the Third Proportional to 85,684 and 133,993

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Solution

The third proportional to 85,684 and 133,993 is: 209,538.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    85,684 : 133,993 = 133,993 : x
  2. Step 2: Convert to fraction form
    85,684/133,993 = 133,993/x
  3. Step 3: Cross multiply
    85,684x = 133,993 × 133,993
  4. Step 4: Simplify right side
    85,684x = 17,954,124,049
  5. Step 5: Solve for x
    x = 17,954,124,049/85,684
  6. Step 6: Final answer
    x = 209,538.82

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.