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Finding the Fourth Proportional to 685.92, 1,029.06 and 411.84

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Solution

The fourth proportional to 685.92, 1,029.06 and 411.84 is: 617.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    685.92 : 1,029.06 = 411.84 : x
  2. Step 2: Convert to fraction form
    685.92/1,029.06 = 411.84/x
  3. Step 3: Cross multiply
    685.92x = 1,029.06 × 411.84
  4. Step 4: Simplify right side
    685.92x = 423,808.07
  5. Step 5: Solve for x
    x = 423,808.07/685.92
  6. Step 6: Final answer
    x = 617.87

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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.