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Finding the Third Proportional to 83,106 and 197,559

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Solution

The third proportional to 83,106 and 197,559 is: 469,635.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,106 : 197,559 = 197,559 : x
  2. Step 2: Convert to fraction form
    83,106/197,559 = 197,559/x
  3. Step 3: Cross multiply
    83,106x = 197,559 × 197,559
  4. Step 4: Simplify right side
    83,106x = 39,029,558,481
  5. Step 5: Solve for x
    x = 39,029,558,481/83,106
  6. Step 6: Final answer
    x = 469,635.87

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.