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Finding the Third Proportional to 512 and 714.75

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Solution

The third proportional to 512 and 714.75 is: 997.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    512 : 714.75 = 714.75 : x
  2. Step 2: Convert to fraction form
    512/714.75 = 714.75/x
  3. Step 3: Cross multiply
    512x = 714.75 × 714.75
  4. Step 4: Simplify right side
    512x = 510,867.56
  5. Step 5: Solve for x
    x = 510,867.56/512
  6. Step 6: Final answer
    x = 997.79

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.