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Finding the Third Proportional to 8,192 and 11,516

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Solution

The third proportional to 8,192 and 11,516 is: 16,188.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,192 : 11,516 = 11,516 : x
  2. Step 2: Convert to fraction form
    8,192/11,516 = 11,516/x
  3. Step 3: Cross multiply
    8,192x = 11,516 × 11,516
  4. Step 4: Simplify right side
    8,192x = 132,618,256
  5. Step 5: Solve for x
    x = 132,618,256/8,192
  6. Step 6: Final answer
    x = 16,188.75

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.