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Finding the Third Proportional to 10,397 and 22,571

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Solution

The third proportional to 10,397 and 22,571 is: 48,999.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,397 : 22,571 = 22,571 : x
  2. Step 2: Convert to fraction form
    10,397/22,571 = 22,571/x
  3. Step 3: Cross multiply
    10,397x = 22,571 × 22,571
  4. Step 4: Simplify right side
    10,397x = 509,450,041
  5. Step 5: Solve for x
    x = 509,450,041/10,397
  6. Step 6: Final answer
    x = 48,999.72

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.