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Finding the Third Proportional to 76,542 and 102,657

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Solution

The third proportional to 76,542 and 102,657 is: 137,682.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,542 : 102,657 = 102,657 : x
  2. Step 2: Convert to fraction form
    76,542/102,657 = 102,657/x
  3. Step 3: Cross multiply
    76,542x = 102,657 × 102,657
  4. Step 4: Simplify right side
    76,542x = 10,538,459,649
  5. Step 5: Solve for x
    x = 10,538,459,649/76,542
  6. Step 6: Final answer
    x = 137,682.05

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.