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Finding the Third Proportional to 20,770 and 32,214

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Solution

The third proportional to 20,770 and 32,214 is: 49,963.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,770 : 32,214 = 32,214 : x
  2. Step 2: Convert to fraction form
    20,770/32,214 = 32,214/x
  3. Step 3: Cross multiply
    20,770x = 32,214 × 32,214
  4. Step 4: Simplify right side
    20,770x = 1,037,741,796
  5. Step 5: Solve for x
    x = 1,037,741,796/20,770
  6. Step 6: Final answer
    x = 49,963.50

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.