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Finding the Third Proportional to 106,711 and 233,102

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Solution

The third proportional to 106,711 and 233,102 is: 509,193.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,711 : 233,102 = 233,102 : x
  2. Step 2: Convert to fraction form
    106,711/233,102 = 233,102/x
  3. Step 3: Cross multiply
    106,711x = 233,102 × 233,102
  4. Step 4: Simplify right side
    106,711x = 54,336,542,404
  5. Step 5: Solve for x
    x = 54,336,542,404/106,711
  6. Step 6: Final answer
    x = 509,193.45

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.