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Finding the Third Proportional to 214.75 and 463.25

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Solution

The third proportional to 214.75 and 463.25 is: 999.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.75 : 463.25 = 463.25 : x
  2. Step 2: Convert to fraction form
    214.75/463.25 = 463.25/x
  3. Step 3: Cross multiply
    214.75x = 463.25 × 463.25
  4. Step 4: Simplify right side
    214.75x = 214,600.56
  5. Step 5: Solve for x
    x = 214,600.56/214.75
  6. Step 6: Final answer
    x = 999.30

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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.