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Finding the Third Proportional to 180 and 197

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Solution

The third proportional to 180 and 197 is: 215.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    180 : 197 = 197 : x
  2. Step 2: Convert to fraction form
    180/197 = 197/x
  3. Step 3: Cross multiply
    180x = 197 × 197
  4. Step 4: Simplify right side
    180x = 38,809
  5. Step 5: Solve for x
    x = 38,809/180
  6. Step 6: Final answer
    x = 215.61

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.