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Finding the Third Proportional to 76,540 and 102,654

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Solution

The third proportional to 76,540 and 102,654 is: 137,677.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,540 : 102,654 = 102,654 : x
  2. Step 2: Convert to fraction form
    76,540/102,654 = 102,654/x
  3. Step 3: Cross multiply
    76,540x = 102,654 × 102,654
  4. Step 4: Simplify right side
    76,540x = 10,537,843,716
  5. Step 5: Solve for x
    x = 10,537,843,716/76,540
  6. Step 6: Final answer
    x = 137,677.60

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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.