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Finding the Third Proportional to 214 and 461.75

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Solution

The third proportional to 214 and 461.75 is: 996.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    214 : 461.75 = 461.75 : x
  2. Step 2: Convert to fraction form
    214/461.75 = 461.75/x
  3. Step 3: Cross multiply
    214x = 461.75 × 461.75
  4. Step 4: Simplify right side
    214x = 213,213.06
  5. Step 5: Solve for x
    x = 213,213.06/214
  6. Step 6: Final answer
    x = 996.32

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.