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Finding the Third Proportional to 205.75 and 457.25

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Solution

The third proportional to 205.75 and 457.25 is: 1,016.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.75 : 457.25 = 457.25 : x
  2. Step 2: Convert to fraction form
    205.75/457.25 = 457.25/x
  3. Step 3: Cross multiply
    205.75x = 457.25 × 457.25
  4. Step 4: Simplify right side
    205.75x = 209,077.56
  5. Step 5: Solve for x
    x = 209,077.56/205.75
  6. Step 6: Final answer
    x = 1,016.17

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.