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Finding the Third Proportional to 38,970 and 82,577

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Solution

The third proportional to 38,970 and 82,577 is: 174,979.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,970 : 82,577 = 82,577 : x
  2. Step 2: Convert to fraction form
    38,970/82,577 = 82,577/x
  3. Step 3: Cross multiply
    38,970x = 82,577 × 82,577
  4. Step 4: Simplify right side
    38,970x = 6,818,960,929
  5. Step 5: Solve for x
    x = 6,818,960,929/38,970
  6. Step 6: Final answer
    x = 174,979.75

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.