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Finding the Third Proportional to 6,509 and 14,206

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Solution

The third proportional to 6,509 and 14,206 is: 31,004.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,509 : 14,206 = 14,206 : x
  2. Step 2: Convert to fraction form
    6,509/14,206 = 14,206/x
  3. Step 3: Cross multiply
    6,509x = 14,206 × 14,206
  4. Step 4: Simplify right side
    6,509x = 201,810,436
  5. Step 5: Solve for x
    x = 201,810,436/6,509
  6. Step 6: Final answer
    x = 31,004.83

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.