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Finding the Third Proportional to 509 and 1,183

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Solution

The third proportional to 509 and 1,183 is: 2,749.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 1,183 = 1,183 : x
  2. Step 2: Convert to fraction form
    509/1,183 = 1,183/x
  3. Step 3: Cross multiply
    509x = 1,183 × 1,183
  4. Step 4: Simplify right side
    509x = 1,399,489
  5. Step 5: Solve for x
    x = 1,399,489/509
  6. Step 6: Final answer
    x = 2,749.49

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.