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Finding the Third Proportional to 209,002 and 313,016

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Solution

The third proportional to 209,002 and 313,016 is: 468,794.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,002 : 313,016 = 313,016 : x
  2. Step 2: Convert to fraction form
    209,002/313,016 = 313,016/x
  3. Step 3: Cross multiply
    209,002x = 313,016 × 313,016
  4. Step 4: Simplify right side
    209,002x = 97,979,016,256
  5. Step 5: Solve for x
    x = 97,979,016,256/209,002
  6. Step 6: Final answer
    x = 468,794.63

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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.