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Finding the Third Proportional to 197.75 and 421.75

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Solution

The third proportional to 197.75 and 421.75 is: 899.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    197.75 : 421.75 = 421.75 : x
  2. Step 2: Convert to fraction form
    197.75/421.75 = 421.75/x
  3. Step 3: Cross multiply
    197.75x = 421.75 × 421.75
  4. Step 4: Simplify right side
    197.75x = 177,873.06
  5. Step 5: Solve for x
    x = 177,873.06/197.75
  6. Step 6: Final answer
    x = 899.48

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.