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Finding the Third Proportional to 523 and 566

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Solution

The third proportional to 523 and 566 is: 612.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 566 = 566 : x
  2. Step 2: Convert to fraction form
    523/566 = 566/x
  3. Step 3: Cross multiply
    523x = 566 × 566
  4. Step 4: Simplify right side
    523x = 320,356
  5. Step 5: Solve for x
    x = 320,356/523
  6. Step 6: Final answer
    x = 612.54

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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.