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Finding the Third Proportional to 214,102 and 470,589

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Solution

The third proportional to 214,102 and 470,589 is: 1,034,338.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,102 : 470,589 = 470,589 : x
  2. Step 2: Convert to fraction form
    214,102/470,589 = 470,589/x
  3. Step 3: Cross multiply
    214,102x = 470,589 × 470,589
  4. Step 4: Simplify right side
    214,102x = 221,454,006,921
  5. Step 5: Solve for x
    x = 221,454,006,921/214,102
  6. Step 6: Final answer
    x = 1,034,338.81

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.