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Finding the Third Proportional to 205.59 and 311.06

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Solution

The third proportional to 205.59 and 311.06 is: 470.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.59 : 311.06 = 311.06 : x
  2. Step 2: Convert to fraction form
    205.59/311.06 = 311.06/x
  3. Step 3: Cross multiply
    205.59x = 311.06 × 311.06
  4. Step 4: Simplify right side
    205.59x = 96,759.88
  5. Step 5: Solve for x
    x = 96,759.88/205.59
  6. Step 6: Final answer
    x = 470.64

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.