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Finding the Fourth Proportional to 1,189.89, 1,784.10 and 409.71

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Solution

The fourth proportional to 1,189.89, 1,784.10 and 409.71 is: 614.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,189.89 : 1,784.10 = 409.71 : x
  2. Step 2: Convert to fraction form
    1,189.89/1,784.10 = 409.71/x
  3. Step 3: Cross multiply
    1,189.89x = 1,784.10 × 409.71
  4. Step 4: Simplify right side
    1,189.89x = 730,963.61
  5. Step 5: Solve for x
    x = 730,963.61/1,189.89
  6. Step 6: Final answer
    x = 614.31

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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.