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Finding the Fourth Proportional to 820.57, 1,231.24 and 409.74

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Solution

The fourth proportional to 820.57, 1,231.24 and 409.74 is: 614.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    820.57 : 1,231.24 = 409.74 : x
  2. Step 2: Convert to fraction form
    820.57/1,231.24 = 409.74/x
  3. Step 3: Cross multiply
    820.57x = 1,231.24 × 409.74
  4. Step 4: Simplify right side
    820.57x = 504,480.07
  5. Step 5: Solve for x
    x = 504,480.07/820.57
  6. Step 6: Final answer
    x = 614.80

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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.