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Finding the Fourth Proportional to 1,412.92, 1,949.64 and 823

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Solution

The fourth proportional to 1,412.92, 1,949.64 and 823 is: 1,135.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,412.92 : 1,949.64 = 823 : x
  2. Step 2: Convert to fraction form
    1,412.92/1,949.64 = 823/x
  3. Step 3: Cross multiply
    1,412.92x = 1,949.64 × 823
  4. Step 4: Simplify right side
    1,412.92x = 1,604,553.72
  5. Step 5: Solve for x
    x = 1,604,553.72/1,412.92
  6. Step 6: Final answer
    x = 1,135.63

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.