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Finding the Third Proportional to 83,072 and 177,019

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Solution

The third proportional to 83,072 and 177,019 is: 377,211.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,072 : 177,019 = 177,019 : x
  2. Step 2: Convert to fraction form
    83,072/177,019 = 177,019/x
  3. Step 3: Cross multiply
    83,072x = 177,019 × 177,019
  4. Step 4: Simplify right side
    83,072x = 31,335,726,361
  5. Step 5: Solve for x
    x = 31,335,726,361/83,072
  6. Step 6: Final answer
    x = 377,211.65

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.