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Finding the Third Proportional to 4,096 and 8,434

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Solution

The third proportional to 4,096 and 8,434 is: 17,366.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,096 : 8,434 = 8,434 : x
  2. Step 2: Convert to fraction form
    4,096/8,434 = 8,434/x
  3. Step 3: Cross multiply
    4,096x = 8,434 × 8,434
  4. Step 4: Simplify right side
    4,096x = 71,132,356
  5. Step 5: Solve for x
    x = 71,132,356/4,096
  6. Step 6: Final answer
    x = 17,366.30

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.