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Finding the Third Proportional to 2,057 and 4,206

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Solution

The third proportional to 2,057 and 4,206 is: 8,600.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,057 : 4,206 = 4,206 : x
  2. Step 2: Convert to fraction form
    2,057/4,206 = 4,206/x
  3. Step 3: Cross multiply
    2,057x = 4,206 × 4,206
  4. Step 4: Simplify right side
    2,057x = 17,690,436
  5. Step 5: Solve for x
    x = 17,690,436/2,057
  6. Step 6: Final answer
    x = 8,600.11

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.