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Finding the Third Proportional to 20,505 and 31,623

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Solution

The third proportional to 20,505 and 31,623 is: 48,769.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,505 : 31,623 = 31,623 : x
  2. Step 2: Convert to fraction form
    20,505/31,623 = 31,623/x
  3. Step 3: Cross multiply
    20,505x = 31,623 × 31,623
  4. Step 4: Simplify right side
    20,505x = 1,000,014,129
  5. Step 5: Solve for x
    x = 1,000,014,129/20,505
  6. Step 6: Final answer
    x = 48,769.28

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.