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Finding the Third Proportional to 205.88 and 457.31

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Solution

The third proportional to 205.88 and 457.31 is: 1,015.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.88 : 457.31 = 457.31 : x
  2. Step 2: Convert to fraction form
    205.88/457.31 = 457.31/x
  3. Step 3: Cross multiply
    205.88x = 457.31 × 457.31
  4. Step 4: Simplify right side
    205.88x = 209,134.72
  5. Step 5: Solve for x
    x = 209,134.72/205.88
  6. Step 6: Final answer
    x = 1,015.83

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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.