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Finding the Third Proportional to 1,009 and 2,048

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Solution

The third proportional to 1,009 and 2,048 is: 4,156.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,009 : 2,048 = 2,048 : x
  2. Step 2: Convert to fraction form
    1,009/2,048 = 2,048/x
  3. Step 3: Cross multiply
    1,009x = 2,048 × 2,048
  4. Step 4: Simplify right side
    1,009x = 4,194,304
  5. Step 5: Solve for x
    x = 4,194,304/1,009
  6. Step 6: Final answer
    x = 4,156.89

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.