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Finding the Third Proportional to 6,538 and 13,423

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Solution

The third proportional to 6,538 and 13,423 is: 27,558.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,538 : 13,423 = 13,423 : x
  2. Step 2: Convert to fraction form
    6,538/13,423 = 13,423/x
  3. Step 3: Cross multiply
    6,538x = 13,423 × 13,423
  4. Step 4: Simplify right side
    6,538x = 180,176,929
  5. Step 5: Solve for x
    x = 180,176,929/6,538
  6. Step 6: Final answer
    x = 27,558.42

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.