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Finding the Third Proportional to 523 and 589

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Solution

The third proportional to 523 and 589 is: 663.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 589 = 589 : x
  2. Step 2: Convert to fraction form
    523/589 = 589/x
  3. Step 3: Cross multiply
    523x = 589 × 589
  4. Step 4: Simplify right side
    523x = 346,921
  5. Step 5: Solve for x
    x = 346,921/523
  6. Step 6: Final answer
    x = 663.33

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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.