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Finding the Fourth Proportional to 512, 706.92 and 409.04

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Solution

The fourth proportional to 512, 706.92 and 409.04 is: 564.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    512 : 706.92 = 409.04 : x
  2. Step 2: Convert to fraction form
    512/706.92 = 409.04/x
  3. Step 3: Cross multiply
    512x = 706.92 × 409.04
  4. Step 4: Simplify right side
    512x = 289,158.56
  5. Step 5: Solve for x
    x = 289,158.56/512
  6. Step 6: Final answer
    x = 564.76

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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.