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Finding the Fourth Proportional to 1,107.71, 1,660.89 and 414.02

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Solution

The fourth proportional to 1,107.71, 1,660.89 and 414.02 is: 620.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,107.71 : 1,660.89 = 414.02 : x
  2. Step 2: Convert to fraction form
    1,107.71/1,660.89 = 414.02/x
  3. Step 3: Cross multiply
    1,107.71x = 1,660.89 × 414.02
  4. Step 4: Simplify right side
    1,107.71x = 687,641.68
  5. Step 5: Solve for x
    x = 687,641.68/1,107.71
  6. Step 6: Final answer
    x = 620.78

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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.