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Finding the Third Proportional to 197.50 and 214.25

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Solution

The third proportional to 197.50 and 214.25 is: 232.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    197.50 : 214.25 = 214.25 : x
  2. Step 2: Convert to fraction form
    197.50/214.25 = 214.25/x
  3. Step 3: Cross multiply
    197.50x = 214.25 × 214.25
  4. Step 4: Simplify right side
    197.50x = 45,903.06
  5. Step 5: Solve for x
    x = 45,903.06/197.50
  6. Step 6: Final answer
    x = 232.42

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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.