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Finding the Fourth Proportional to 512.40, 706.80 and 414

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Solution

The fourth proportional to 512.40, 706.80 and 414 is: 571.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    512.40 : 706.80 = 414 : x
  2. Step 2: Convert to fraction form
    512.40/706.80 = 414/x
  3. Step 3: Cross multiply
    512.40x = 706.80 × 414
  4. Step 4: Simplify right side
    512.40x = 292,615.20
  5. Step 5: Solve for x
    x = 292,615.20/512.40
  6. Step 6: Final answer
    x = 571.07

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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.