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Finding the Third Proportional to 213.84 and 405.75

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Solution

The third proportional to 213.84 and 405.75 is: 769.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.84 : 405.75 = 405.75 : x
  2. Step 2: Convert to fraction form
    213.84/405.75 = 405.75/x
  3. Step 3: Cross multiply
    213.84x = 405.75 × 405.75
  4. Step 4: Simplify right side
    213.84x = 164,633.06
  5. Step 5: Solve for x
    x = 164,633.06/213.84
  6. Step 6: Final answer
    x = 769.88

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Why These Related Problems?

These problems maintain the same ratio (1.90) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.