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Finding the Third Proportional to 585 and 689

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Solution

The third proportional to 585 and 689 is: 811.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    585 : 689 = 689 : x
  2. Step 2: Convert to fraction form
    585/689 = 689/x
  3. Step 3: Cross multiply
    585x = 689 × 689
  4. Step 4: Simplify right side
    585x = 474,721
  5. Step 5: Solve for x
    x = 474,721/585
  6. Step 6: Final answer
    x = 811.49

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.