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Finding the Third Proportional to 76,786 and 102,075

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Solution

The third proportional to 76,786 and 102,075 is: 135,692.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,786 : 102,075 = 102,075 : x
  2. Step 2: Convert to fraction form
    76,786/102,075 = 102,075/x
  3. Step 3: Cross multiply
    76,786x = 102,075 × 102,075
  4. Step 4: Simplify right side
    76,786x = 10,419,305,625
  5. Step 5: Solve for x
    x = 10,419,305,625/76,786
  6. Step 6: Final answer
    x = 135,692.78

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.