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Finding the Fourth Proportional to 1,102.26, 1,654.04 and 409.42

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Solution

The fourth proportional to 1,102.26, 1,654.04 and 409.42 is: 614.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102.26 : 1,654.04 = 409.42 : x
  2. Step 2: Convert to fraction form
    1,102.26/1,654.04 = 409.42/x
  3. Step 3: Cross multiply
    1,102.26x = 1,654.04 × 409.42
  4. Step 4: Simplify right side
    1,102.26x = 677,197.06
  5. Step 5: Solve for x
    x = 677,197.06/1,102.26
  6. Step 6: Final answer
    x = 614.37

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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.