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Finding the Third Proportional to 82,098 and 177,294

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Solution

The third proportional to 82,098 and 177,294 is: 382,873.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,098 : 177,294 = 177,294 : x
  2. Step 2: Convert to fraction form
    82,098/177,294 = 177,294/x
  3. Step 3: Cross multiply
    82,098x = 177,294 × 177,294
  4. Step 4: Simplify right side
    82,098x = 31,433,162,436
  5. Step 5: Solve for x
    x = 31,433,162,436/82,098
  6. Step 6: Final answer
    x = 382,873.67

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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.