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Finding the Third Proportional to 8,192 and 11,541

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Solution

The third proportional to 8,192 and 11,541 is: 16,259.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,192 : 11,541 = 11,541 : x
  2. Step 2: Convert to fraction form
    8,192/11,541 = 11,541/x
  3. Step 3: Cross multiply
    8,192x = 11,541 × 11,541
  4. Step 4: Simplify right side
    8,192x = 133,194,681
  5. Step 5: Solve for x
    x = 133,194,681/8,192
  6. Step 6: Final answer
    x = 16,259.12

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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.