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Finding the Third Proportional to 5,478 and 13,206

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Solution

The third proportional to 5,478 and 13,206 is: 31,836.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,478 : 13,206 = 13,206 : x
  2. Step 2: Convert to fraction form
    5,478/13,206 = 13,206/x
  3. Step 3: Cross multiply
    5,478x = 13,206 × 13,206
  4. Step 4: Simplify right side
    5,478x = 174,398,436
  5. Step 5: Solve for x
    x = 174,398,436/5,478
  6. Step 6: Final answer
    x = 31,836.15

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.