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Finding the Fourth Proportional to 1,102.69, 1,654.04 and 409.33

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Solution

The fourth proportional to 1,102.69, 1,654.04 and 409.33 is: 614.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102.69 : 1,654.04 = 409.33 : x
  2. Step 2: Convert to fraction form
    1,102.69/1,654.04 = 409.33/x
  3. Step 3: Cross multiply
    1,102.69x = 1,654.04 × 409.33
  4. Step 4: Simplify right side
    1,102.69x = 677,048.19
  5. Step 5: Solve for x
    x = 677,048.19/1,102.69
  6. Step 6: Final answer
    x = 614.00

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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.