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Finding the Fourth Proportional to 741, 1,022.56 and 409.42

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Solution

The fourth proportional to 741, 1,022.56 and 409.42 is: 564.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    741 : 1,022.56 = 409.42 : x
  2. Step 2: Convert to fraction form
    741/1,022.56 = 409.42/x
  3. Step 3: Cross multiply
    741x = 1,022.56 × 409.42
  4. Step 4: Simplify right side
    741x = 418,656.52
  5. Step 5: Solve for x
    x = 418,656.52/741
  6. Step 6: Final answer
    x = 564.99

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.