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Finding the Third Proportional to 214.31 and 464.06

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Solution

The third proportional to 214.31 and 464.06 is: 1,004.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.31 : 464.06 = 464.06 : x
  2. Step 2: Convert to fraction form
    214.31/464.06 = 464.06/x
  3. Step 3: Cross multiply
    214.31x = 464.06 × 464.06
  4. Step 4: Simplify right side
    214.31x = 215,354.00
  5. Step 5: Solve for x
    x = 215,354.00/214.31
  6. Step 6: Final answer
    x = 1,004.86

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.