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Finding the Third Proportional to 213,410 and 457,924

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Solution

The third proportional to 213,410 and 457,924 is: 982,589.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,410 : 457,924 = 457,924 : x
  2. Step 2: Convert to fraction form
    213,410/457,924 = 457,924/x
  3. Step 3: Cross multiply
    213,410x = 457,924 × 457,924
  4. Step 4: Simplify right side
    213,410x = 209,694,389,776
  5. Step 5: Solve for x
    x = 209,694,389,776/213,410
  6. Step 6: Final answer
    x = 982,589.33

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.