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Finding the Third Proportional to 709 and 782

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Solution

The third proportional to 709 and 782 is: 862.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    709 : 782 = 782 : x
  2. Step 2: Convert to fraction form
    709/782 = 782/x
  3. Step 3: Cross multiply
    709x = 782 × 782
  4. Step 4: Simplify right side
    709x = 611,524
  5. Step 5: Solve for x
    x = 611,524/709
  6. Step 6: Final answer
    x = 862.52

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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.