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Finding the Third Proportional to 120 and 214

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Solution

The third proportional to 120 and 214 is: 381.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    120 : 214 = 214 : x
  2. Step 2: Convert to fraction form
    120/214 = 214/x
  3. Step 3: Cross multiply
    120x = 214 × 214
  4. Step 4: Simplify right side
    120x = 45,796
  5. Step 5: Solve for x
    x = 45,796/120
  6. Step 6: Final answer
    x = 381.63

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.