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Finding the Fourth Proportional to 821.00, 1,229.96 and 409.65

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Solution

The fourth proportional to 821.00, 1,229.96 and 409.65 is: 613.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.00 : 1,229.96 = 409.65 : x
  2. Step 2: Convert to fraction form
    821.00/1,229.96 = 409.65/x
  3. Step 3: Cross multiply
    821.00x = 1,229.96 × 409.65
  4. Step 4: Simplify right side
    821.00x = 503,853.11
  5. Step 5: Solve for x
    x = 503,853.11/821.00
  6. Step 6: Final answer
    x = 613.71

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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.