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Finding the Third Proportional to 77.50 and 178.75

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Solution

The third proportional to 77.50 and 178.75 is: 412.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    77.50 : 178.75 = 178.75 : x
  2. Step 2: Convert to fraction form
    77.50/178.75 = 178.75/x
  3. Step 3: Cross multiply
    77.50x = 178.75 × 178.75
  4. Step 4: Simplify right side
    77.50x = 31,951.56
  5. Step 5: Solve for x
    x = 31,951.56/77.50
  6. Step 6: Final answer
    x = 412.28

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.