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Finding the Fourth Proportional to 2,121.40, 3,182.82 and 823

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Solution

The fourth proportional to 2,121.40, 3,182.82 and 823 is: 1,234.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,121.40 : 3,182.82 = 823 : x
  2. Step 2: Convert to fraction form
    2,121.40/3,182.82 = 823/x
  3. Step 3: Cross multiply
    2,121.40x = 3,182.82 × 823
  4. Step 4: Simplify right side
    2,121.40x = 2,619,460.86
  5. Step 5: Solve for x
    x = 2,619,460.86/2,121.40
  6. Step 6: Final answer
    x = 1,234.78

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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.