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Finding the Third Proportional to 706 and 777

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Solution

The third proportional to 706 and 777 is: 855.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    706 : 777 = 777 : x
  2. Step 2: Convert to fraction form
    706/777 = 777/x
  3. Step 3: Cross multiply
    706x = 777 × 777
  4. Step 4: Simplify right side
    706x = 603,729
  5. Step 5: Solve for x
    x = 603,729/706
  6. Step 6: Final answer
    x = 855.14

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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.