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Finding the Fourth Proportional to 1,383.66, 2,075.82 and 409.74

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Solution

The fourth proportional to 1,383.66, 2,075.82 and 409.74 is: 614.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,383.66 : 2,075.82 = 409.74 : x
  2. Step 2: Convert to fraction form
    1,383.66/2,075.82 = 409.74/x
  3. Step 3: Cross multiply
    1,383.66x = 2,075.82 × 409.74
  4. Step 4: Simplify right side
    1,383.66x = 850,546.49
  5. Step 5: Solve for x
    x = 850,546.49/1,383.66
  6. Step 6: Final answer
    x = 614.71

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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.