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Finding the Fourth Proportional to 512.85, 706.92 and 419.43

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Solution

The fourth proportional to 512.85, 706.92 and 419.43 is: 578.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    512.85 : 706.92 = 419.43 : x
  2. Step 2: Convert to fraction form
    512.85/706.92 = 419.43/x
  3. Step 3: Cross multiply
    512.85x = 706.92 × 419.43
  4. Step 4: Simplify right side
    512.85x = 296,503.46
  5. Step 5: Solve for x
    x = 296,503.46/512.85
  6. Step 6: Final answer
    x = 578.15

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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.