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Finding the Third Proportional to 76,784 and 102,072

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Solution

The third proportional to 76,784 and 102,072 is: 135,688.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,784 : 102,072 = 102,072 : x
  2. Step 2: Convert to fraction form
    76,784/102,072 = 102,072/x
  3. Step 3: Cross multiply
    76,784x = 102,072 × 102,072
  4. Step 4: Simplify right side
    76,784x = 10,418,693,184
  5. Step 5: Solve for x
    x = 10,418,693,184/76,784
  6. Step 6: Final answer
    x = 135,688.34

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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.