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Finding the Fourth Proportional to 512.69, 767.93 and 409.41

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Solution

The fourth proportional to 512.69, 767.93 and 409.41 is: 613.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    512.69 : 767.93 = 409.41 : x
  2. Step 2: Convert to fraction form
    512.69/767.93 = 409.41/x
  3. Step 3: Cross multiply
    512.69x = 767.93 × 409.41
  4. Step 4: Simplify right side
    512.69x = 314,396.17
  5. Step 5: Solve for x
    x = 314,396.17/512.69
  6. Step 6: Final answer
    x = 613.23

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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.