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Finding the Third Proportional to 197.75 and 214.50

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Solution

The third proportional to 197.75 and 214.50 is: 232.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    197.75 : 214.50 = 214.50 : x
  2. Step 2: Convert to fraction form
    197.75/214.50 = 214.50/x
  3. Step 3: Cross multiply
    197.75x = 214.50 × 214.50
  4. Step 4: Simplify right side
    197.75x = 46,010.25
  5. Step 5: Solve for x
    x = 46,010.25/197.75
  6. Step 6: Final answer
    x = 232.67

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.