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Finding the Third Proportional to 523 and 609

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Solution

The third proportional to 523 and 609 is: 709.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 609 = 609 : x
  2. Step 2: Convert to fraction form
    523/609 = 609/x
  3. Step 3: Cross multiply
    523x = 609 × 609
  4. Step 4: Simplify right side
    523x = 370,881
  5. Step 5: Solve for x
    x = 370,881/523
  6. Step 6: Final answer
    x = 709.14

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.