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Finding the Third Proportional to 10,424 and 13,206

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Solution

The third proportional to 10,424 and 13,206 is: 16,730.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,424 : 13,206 = 13,206 : x
  2. Step 2: Convert to fraction form
    10,424/13,206 = 13,206/x
  3. Step 3: Cross multiply
    10,424x = 13,206 × 13,206
  4. Step 4: Simplify right side
    10,424x = 174,398,436
  5. Step 5: Solve for x
    x = 174,398,436/10,424
  6. Step 6: Final answer
    x = 16,730.47

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.