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Finding the Fourth Proportional to 800.53, 1,200.24 and 409.77

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Solution

The fourth proportional to 800.53, 1,200.24 and 409.77 is: 614.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    800.53 : 1,200.24 = 409.77 : x
  2. Step 2: Convert to fraction form
    800.53/1,200.24 = 409.77/x
  3. Step 3: Cross multiply
    800.53x = 1,200.24 × 409.77
  4. Step 4: Simplify right side
    800.53x = 491,822.34
  5. Step 5: Solve for x
    x = 491,822.34/800.53
  6. Step 6: Final answer
    x = 614.37

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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.