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Finding the Third Proportional to 82,413 and 177,966

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Solution

The third proportional to 82,413 and 177,966 is: 384,307.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,413 : 177,966 = 177,966 : x
  2. Step 2: Convert to fraction form
    82,413/177,966 = 177,966/x
  3. Step 3: Cross multiply
    82,413x = 177,966 × 177,966
  4. Step 4: Simplify right side
    82,413x = 31,671,897,156
  5. Step 5: Solve for x
    x = 31,671,897,156/82,413
  6. Step 6: Final answer
    x = 384,307.05

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.