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Finding the Third Proportional to 314,498 and 419,004

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Solution

The third proportional to 314,498 and 419,004 is: 558,236.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    314,498 : 419,004 = 419,004 : x
  2. Step 2: Convert to fraction form
    314,498/419,004 = 419,004/x
  3. Step 3: Cross multiply
    314,498x = 419,004 × 419,004
  4. Step 4: Simplify right side
    314,498x = 175,564,352,016
  5. Step 5: Solve for x
    x = 175,564,352,016/314,498
  6. Step 6: Final answer
    x = 558,236.78

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.