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Finding the Third Proportional to 493 and 591

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Solution

The third proportional to 493 and 591 is: 708.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    493 : 591 = 591 : x
  2. Step 2: Convert to fraction form
    493/591 = 591/x
  3. Step 3: Cross multiply
    493x = 591 × 591
  4. Step 4: Simplify right side
    493x = 349,281
  5. Step 5: Solve for x
    x = 349,281/493
  6. Step 6: Final answer
    x = 708.48

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.