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Finding the Third Proportional to 205.94 and 311.72

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Solution

The third proportional to 205.94 and 311.72 is: 471.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.94 : 311.72 = 311.72 : x
  2. Step 2: Convert to fraction form
    205.94/311.72 = 311.72/x
  3. Step 3: Cross multiply
    205.94x = 311.72 × 311.72
  4. Step 4: Simplify right side
    205.94x = 97,168.58
  5. Step 5: Solve for x
    x = 97,168.58/205.94
  6. Step 6: Final answer
    x = 471.84

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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.