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Finding the Third Proportional to 12,971 and 20,591

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Solution

The third proportional to 12,971 and 20,591 is: 32,687.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,971 : 20,591 = 20,591 : x
  2. Step 2: Convert to fraction form
    12,971/20,591 = 20,591/x
  3. Step 3: Cross multiply
    12,971x = 20,591 × 20,591
  4. Step 4: Simplify right side
    12,971x = 423,989,281
  5. Step 5: Solve for x
    x = 423,989,281/12,971
  6. Step 6: Final answer
    x = 32,687.48

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.