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Finding the Third Proportional to 657 and 709

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Solution

The third proportional to 657 and 709 is: 765.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    657 : 709 = 709 : x
  2. Step 2: Convert to fraction form
    657/709 = 709/x
  3. Step 3: Cross multiply
    657x = 709 × 709
  4. Step 4: Simplify right side
    657x = 502,681
  5. Step 5: Solve for x
    x = 502,681/657
  6. Step 6: Final answer
    x = 765.12

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.