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Finding the Third Proportional to 509 and 762

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Solution

The third proportional to 509 and 762 is: 1,140.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 762 = 762 : x
  2. Step 2: Convert to fraction form
    509/762 = 762/x
  3. Step 3: Cross multiply
    509x = 762 × 762
  4. Step 4: Simplify right side
    509x = 580,644
  5. Step 5: Solve for x
    x = 580,644/509
  6. Step 6: Final answer
    x = 1,140.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.