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Finding the Third Proportional to 205.75 and 313.25

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Solution

The third proportional to 205.75 and 313.25 is: 476.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.75 : 313.25 = 313.25 : x
  2. Step 2: Convert to fraction form
    205.75/313.25 = 313.25/x
  3. Step 3: Cross multiply
    205.75x = 313.25 × 313.25
  4. Step 4: Simplify right side
    205.75x = 98,125.56
  5. Step 5: Solve for x
    x = 98,125.56/205.75
  6. Step 6: Final answer
    x = 476.92

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.