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Finding the Third Proportional to 413,224 and 584,908

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Solution

The third proportional to 413,224 and 584,908 is: 827,922.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,224 : 584,908 = 584,908 : x
  2. Step 2: Convert to fraction form
    413,224/584,908 = 584,908/x
  3. Step 3: Cross multiply
    413,224x = 584,908 × 584,908
  4. Step 4: Simplify right side
    413,224x = 342,117,368,464
  5. Step 5: Solve for x
    x = 342,117,368,464/413,224
  6. Step 6: Final answer
    x = 827,922.31

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.