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Finding the Third Proportional to 106.78 and 232.31

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Solution

The third proportional to 106.78 and 232.31 is: 505.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.78 : 232.31 = 232.31 : x
  2. Step 2: Convert to fraction form
    106.78/232.31 = 232.31/x
  3. Step 3: Cross multiply
    106.78x = 232.31 × 232.31
  4. Step 4: Simplify right side
    106.78x = 53,969.10
  5. Step 5: Solve for x
    x = 53,969.10/106.78
  6. Step 6: Final answer
    x = 505.42

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.