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Finding the Third Proportional to 6,197 and 13,523

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Solution

The third proportional to 6,197 and 13,523 is: 29,509.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,197 : 13,523 = 13,523 : x
  2. Step 2: Convert to fraction form
    6,197/13,523 = 13,523/x
  3. Step 3: Cross multiply
    6,197x = 13,523 × 13,523
  4. Step 4: Simplify right side
    6,197x = 182,871,529
  5. Step 5: Solve for x
    x = 182,871,529/6,197
  6. Step 6: Final answer
    x = 29,509.69

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.