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Finding the Third Proportional to 569 and 642

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Solution

The third proportional to 569 and 642 is: 724.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    569 : 642 = 642 : x
  2. Step 2: Convert to fraction form
    569/642 = 642/x
  3. Step 3: Cross multiply
    569x = 642 × 642
  4. Step 4: Simplify right side
    569x = 412,164
  5. Step 5: Solve for x
    x = 412,164/569
  6. Step 6: Final answer
    x = 724.37

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.