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Finding the Third Proportional to 205.75 and 308.50

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Solution

The third proportional to 205.75 and 308.50 is: 462.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.75 : 308.50 = 308.50 : x
  2. Step 2: Convert to fraction form
    205.75/308.50 = 308.50/x
  3. Step 3: Cross multiply
    205.75x = 308.50 × 308.50
  4. Step 4: Simplify right side
    205.75x = 95,172.25
  5. Step 5: Solve for x
    x = 95,172.25/205.75
  6. Step 6: Final answer
    x = 462.56

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.