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Finding the Third Proportional to 76.78 and 120.23

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Solution

The third proportional to 76.78 and 120.23 is: 188.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    76.78 : 120.23 = 120.23 : x
  2. Step 2: Convert to fraction form
    76.78/120.23 = 120.23/x
  3. Step 3: Cross multiply
    76.78x = 120.23 × 120.23
  4. Step 4: Simplify right side
    76.78x = 14,456.30
  5. Step 5: Solve for x
    x = 14,456.30/76.78
  6. Step 6: Final answer
    x = 188.28

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.