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Finding the Fourth Proportional to 1,105.34, 1,657.94 and 411.74

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Solution

The fourth proportional to 1,105.34, 1,657.94 and 411.74 is: 617.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,105.34 : 1,657.94 = 411.74 : x
  2. Step 2: Convert to fraction form
    1,105.34/1,657.94 = 411.74/x
  3. Step 3: Cross multiply
    1,105.34x = 1,657.94 × 411.74
  4. Step 4: Simplify right side
    1,105.34x = 682,629.87
  5. Step 5: Solve for x
    x = 682,629.87/1,105.34
  6. Step 6: Final answer
    x = 617.58

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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.