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Finding the Third Proportional to 705.75 and 774.75

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Solution

The third proportional to 705.75 and 774.75 is: 850.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    705.75 : 774.75 = 774.75 : x
  2. Step 2: Convert to fraction form
    705.75/774.75 = 774.75/x
  3. Step 3: Cross multiply
    705.75x = 774.75 × 774.75
  4. Step 4: Simplify right side
    705.75x = 600,237.56
  5. Step 5: Solve for x
    x = 600,237.56/705.75
  6. Step 6: Final answer
    x = 850.50

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.