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Finding the Third Proportional to 83,051 and 194,973

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Solution

The third proportional to 83,051 and 194,973 is: 457,724.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,051 : 194,973 = 194,973 : x
  2. Step 2: Convert to fraction form
    83,051/194,973 = 194,973/x
  3. Step 3: Cross multiply
    83,051x = 194,973 × 194,973
  4. Step 4: Simplify right side
    83,051x = 38,014,470,729
  5. Step 5: Solve for x
    x = 38,014,470,729/83,051
  6. Step 6: Final answer
    x = 457,724.42

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.