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Finding the Third Proportional to 51,023 and 76,729

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Solution

The third proportional to 51,023 and 76,729 is: 115,385.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,023 : 76,729 = 76,729 : x
  2. Step 2: Convert to fraction form
    51,023/76,729 = 76,729/x
  3. Step 3: Cross multiply
    51,023x = 76,729 × 76,729
  4. Step 4: Simplify right side
    51,023x = 5,887,339,441
  5. Step 5: Solve for x
    x = 5,887,339,441/51,023
  6. Step 6: Final answer
    x = 115,385.99

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.