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Finding the Third Proportional to 10,397 and 22,465

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Solution

The third proportional to 10,397 and 22,465 is: 48,540.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,397 : 22,465 = 22,465 : x
  2. Step 2: Convert to fraction form
    10,397/22,465 = 22,465/x
  3. Step 3: Cross multiply
    10,397x = 22,465 × 22,465
  4. Step 4: Simplify right side
    10,397x = 504,676,225
  5. Step 5: Solve for x
    x = 504,676,225/10,397
  6. Step 6: Final answer
    x = 48,540.56

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.