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Finding the Fourth Proportional to 1,605.87, 2,409 and 509.84

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Solution

The fourth proportional to 1,605.87, 2,409 and 509.84 is: 764.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,605.87 : 2,409 = 509.84 : x
  2. Step 2: Convert to fraction form
    1,605.87/2,409 = 509.84/x
  3. Step 3: Cross multiply
    1,605.87x = 2,409 × 509.84
  4. Step 4: Simplify right side
    1,605.87x = 1,228,204.56
  5. Step 5: Solve for x
    x = 1,228,204.56/1,605.87
  6. Step 6: Final answer
    x = 764.82

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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.