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Finding the Third Proportional to 3,206 and 4,097

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Solution

The third proportional to 3,206 and 4,097 is: 5,235.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,206 : 4,097 = 4,097 : x
  2. Step 2: Convert to fraction form
    3,206/4,097 = 4,097/x
  3. Step 3: Cross multiply
    3,206x = 4,097 × 4,097
  4. Step 4: Simplify right side
    3,206x = 16,785,409
  5. Step 5: Solve for x
    x = 16,785,409/3,206
  6. Step 6: Final answer
    x = 5,235.62

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.