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Finding the Fourth Proportional to 1,189.42, 1,784.34 and 409.50

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Solution

The fourth proportional to 1,189.42, 1,784.34 and 409.50 is: 614.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,189.42 : 1,784.34 = 409.50 : x
  2. Step 2: Convert to fraction form
    1,189.42/1,784.34 = 409.50/x
  3. Step 3: Cross multiply
    1,189.42x = 1,784.34 × 409.50
  4. Step 4: Simplify right side
    1,189.42x = 730,692.39
  5. Step 5: Solve for x
    x = 730,692.39/1,189.42
  6. Step 6: Final answer
    x = 614.33

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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.