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Finding the Third Proportional to 51,410 and 81,471

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Solution

The third proportional to 51,410 and 81,471 is: 129,109.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,410 : 81,471 = 81,471 : x
  2. Step 2: Convert to fraction form
    51,410/81,471 = 81,471/x
  3. Step 3: Cross multiply
    51,410x = 81,471 × 81,471
  4. Step 4: Simplify right side
    51,410x = 6,637,523,841
  5. Step 5: Solve for x
    x = 6,637,523,841/51,410
  6. Step 6: Final answer
    x = 129,109.59

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.