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Finding the Third Proportional to 214,827 and 470,967

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Solution

The third proportional to 214,827 and 470,967 is: 1,032,504.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,827 : 470,967 = 470,967 : x
  2. Step 2: Convert to fraction form
    214,827/470,967 = 470,967/x
  3. Step 3: Cross multiply
    214,827x = 470,967 × 470,967
  4. Step 4: Simplify right side
    214,827x = 221,809,915,089
  5. Step 5: Solve for x
    x = 221,809,915,089/214,827
  6. Step 6: Final answer
    x = 1,032,504.83

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.