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Finding the Third Proportional to 205.88 and 365.06

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Solution

The third proportional to 205.88 and 365.06 is: 647.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.88 : 365.06 = 365.06 : x
  2. Step 2: Convert to fraction form
    205.88/365.06 = 365.06/x
  3. Step 3: Cross multiply
    205.88x = 365.06 × 365.06
  4. Step 4: Simplify right side
    205.88x = 133,270.63
  5. Step 5: Solve for x
    x = 133,270.63/205.88
  6. Step 6: Final answer
    x = 647.34

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.