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Finding the Third Proportional to 76,806 and 177,921

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Solution

The third proportional to 76,806 and 177,921 is: 412,153.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,806 : 177,921 = 177,921 : x
  2. Step 2: Convert to fraction form
    76,806/177,921 = 177,921/x
  3. Step 3: Cross multiply
    76,806x = 177,921 × 177,921
  4. Step 4: Simplify right side
    76,806x = 31,655,882,241
  5. Step 5: Solve for x
    x = 31,655,882,241/76,806
  6. Step 6: Final answer
    x = 412,153.77

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.