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Finding the Third Proportional to 193,838 and 411,162

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Solution

The third proportional to 193,838 and 411,162 is: 872,141.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    193,838 : 411,162 = 411,162 : x
  2. Step 2: Convert to fraction form
    193,838/411,162 = 411,162/x
  3. Step 3: Cross multiply
    193,838x = 411,162 × 411,162
  4. Step 4: Simplify right side
    193,838x = 169,054,190,244
  5. Step 5: Solve for x
    x = 169,054,190,244/193,838
  6. Step 6: Final answer
    x = 872,141.63

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.