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Finding the Third Proportional to 102 and 217

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Solution

The third proportional to 102 and 217 is: 461.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    102 : 217 = 217 : x
  2. Step 2: Convert to fraction form
    102/217 = 217/x
  3. Step 3: Cross multiply
    102x = 217 × 217
  4. Step 4: Simplify right side
    102x = 47,089
  5. Step 5: Solve for x
    x = 47,089/102
  6. Step 6: Final answer
    x = 461.66

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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.