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Finding the Third Proportional to 205.78 and 310.78

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Solution

The third proportional to 205.78 and 310.78 is: 469.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.78 : 310.78 = 310.78 : x
  2. Step 2: Convert to fraction form
    205.78/310.78 = 310.78/x
  3. Step 3: Cross multiply
    205.78x = 310.78 × 310.78
  4. Step 4: Simplify right side
    205.78x = 96,584.99
  5. Step 5: Solve for x
    x = 96,584.99/205.78
  6. Step 6: Final answer
    x = 469.36

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.