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Finding the Third Proportional to 678 and 765.75

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Solution

The third proportional to 678 and 765.75 is: 864.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    678 : 765.75 = 765.75 : x
  2. Step 2: Convert to fraction form
    678/765.75 = 765.75/x
  3. Step 3: Cross multiply
    678x = 765.75 × 765.75
  4. Step 4: Simplify right side
    678x = 586,373.06
  5. Step 5: Solve for x
    x = 586,373.06/678
  6. Step 6: Final answer
    x = 864.86

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.