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Finding the Third Proportional to 82,580 and 178,408

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Solution

The third proportional to 82,580 and 178,408 is: 385,437.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,580 : 178,408 = 178,408 : x
  2. Step 2: Convert to fraction form
    82,580/178,408 = 178,408/x
  3. Step 3: Cross multiply
    82,580x = 178,408 × 178,408
  4. Step 4: Simplify right side
    82,580x = 31,829,414,464
  5. Step 5: Solve for x
    x = 31,829,414,464/82,580
  6. Step 6: Final answer
    x = 385,437.33

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.