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Finding the Third Proportional to 523 and 569

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Solution

The third proportional to 523 and 569 is: 619.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 569 = 569 : x
  2. Step 2: Convert to fraction form
    523/569 = 569/x
  3. Step 3: Cross multiply
    523x = 569 × 569
  4. Step 4: Simplify right side
    523x = 323,761
  5. Step 5: Solve for x
    x = 323,761/523
  6. Step 6: Final answer
    x = 619.05

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.