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Finding the Third Proportional to 229.78 and 311.06

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Solution

The third proportional to 229.78 and 311.06 is: 421.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    229.78 : 311.06 = 311.06 : x
  2. Step 2: Convert to fraction form
    229.78/311.06 = 311.06/x
  3. Step 3: Cross multiply
    229.78x = 311.06 × 311.06
  4. Step 4: Simplify right side
    229.78x = 96,759.88
  5. Step 5: Solve for x
    x = 96,759.88/229.78
  6. Step 6: Final answer
    x = 421.10

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.