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Finding the Third Proportional to 709 and 857

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Solution

The third proportional to 709 and 857 is: 1,035.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    709 : 857 = 857 : x
  2. Step 2: Convert to fraction form
    709/857 = 857/x
  3. Step 3: Cross multiply
    709x = 857 × 857
  4. Step 4: Simplify right side
    709x = 734,449
  5. Step 5: Solve for x
    x = 734,449/709
  6. Step 6: Final answer
    x = 1,035.89

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.