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Finding the Third Proportional to 6,564 and 14,384

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Solution

The third proportional to 6,564 and 14,384 is: 31,520.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,564 : 14,384 = 14,384 : x
  2. Step 2: Convert to fraction form
    6,564/14,384 = 14,384/x
  3. Step 3: Cross multiply
    6,564x = 14,384 × 14,384
  4. Step 4: Simplify right side
    6,564x = 206,899,456
  5. Step 5: Solve for x
    x = 206,899,456/6,564
  6. Step 6: Final answer
    x = 31,520.33

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.