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Finding the Third Proportional to 81,411 and 103,486

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Solution

The third proportional to 81,411 and 103,486 is: 131,546.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,411 : 103,486 = 103,486 : x
  2. Step 2: Convert to fraction form
    81,411/103,486 = 103,486/x
  3. Step 3: Cross multiply
    81,411x = 103,486 × 103,486
  4. Step 4: Simplify right side
    81,411x = 10,709,352,196
  5. Step 5: Solve for x
    x = 10,709,352,196/81,411
  6. Step 6: Final answer
    x = 131,546.75

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.