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Finding the Fourth Proportional to 1,383.57, 2,075.76 and 409.70

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Solution

The fourth proportional to 1,383.57, 2,075.76 and 409.70 is: 614.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,383.57 : 2,075.76 = 409.70 : x
  2. Step 2: Convert to fraction form
    1,383.57/2,075.76 = 409.70/x
  3. Step 3: Cross multiply
    1,383.57x = 2,075.76 × 409.70
  4. Step 4: Simplify right side
    1,383.57x = 850,428.49
  5. Step 5: Solve for x
    x = 850,428.49/1,383.57
  6. Step 6: Final answer
    x = 614.66

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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.