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Finding the Third Proportional to 49.78 and 102.09

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Solution

The third proportional to 49.78 and 102.09 is: 209.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    49.78 : 102.09 = 102.09 : x
  2. Step 2: Convert to fraction form
    49.78/102.09 = 102.09/x
  3. Step 3: Cross multiply
    49.78x = 102.09 × 102.09
  4. Step 4: Simplify right side
    49.78x = 10,423.13
  5. Step 5: Solve for x
    x = 10,423.13/49.78
  6. Step 6: Final answer
    x = 209.38

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.