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Finding the Fourth Proportional to 823.69, 1,234.97 and 310.25

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Solution

The fourth proportional to 823.69, 1,234.97 and 310.25 is: 465.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.69 : 1,234.97 = 310.25 : x
  2. Step 2: Convert to fraction form
    823.69/1,234.97 = 310.25/x
  3. Step 3: Cross multiply
    823.69x = 1,234.97 × 310.25
  4. Step 4: Simplify right side
    823.69x = 383,149.44
  5. Step 5: Solve for x
    x = 383,149.44/823.69
  6. Step 6: Final answer
    x = 465.16

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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.