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Finding the Fourth Proportional to 1,605.38, 2,408.31 and 509.78

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Solution

The fourth proportional to 1,605.38, 2,408.31 and 509.78 is: 764.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,605.38 : 2,408.31 = 509.78 : x
  2. Step 2: Convert to fraction form
    1,605.38/2,408.31 = 509.78/x
  3. Step 3: Cross multiply
    1,605.38x = 2,408.31 × 509.78
  4. Step 4: Simplify right side
    1,605.38x = 1,227,708.27
  5. Step 5: Solve for x
    x = 1,227,708.27/1,605.38
  6. Step 6: Final answer
    x = 764.75

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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.