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Finding the Third Proportional to 205.78 and 455.06

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Solution

The third proportional to 205.78 and 455.06 is: 1,006.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.78 : 455.06 = 455.06 : x
  2. Step 2: Convert to fraction form
    205.78/455.06 = 455.06/x
  3. Step 3: Cross multiply
    205.78x = 455.06 × 455.06
  4. Step 4: Simplify right side
    205.78x = 207,081.88
  5. Step 5: Solve for x
    x = 207,081.88/205.78
  6. Step 6: Final answer
    x = 1,006.32

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.