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Finding the Third Proportional to 214 and 467

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Solution

The third proportional to 214 and 467 is: 1,019.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    214 : 467 = 467 : x
  2. Step 2: Convert to fraction form
    214/467 = 467/x
  3. Step 3: Cross multiply
    214x = 467 × 467
  4. Step 4: Simplify right side
    214x = 218,089
  5. Step 5: Solve for x
    x = 218,089/214
  6. Step 6: Final answer
    x = 1,019.11

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.