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Finding the Third Proportional to 82,409 and 176,482

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Solution

The third proportional to 82,409 and 176,482 is: 377,942.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,409 : 176,482 = 176,482 : x
  2. Step 2: Convert to fraction form
    82,409/176,482 = 176,482/x
  3. Step 3: Cross multiply
    82,409x = 176,482 × 176,482
  4. Step 4: Simplify right side
    82,409x = 31,145,896,324
  5. Step 5: Solve for x
    x = 31,145,896,324/82,409
  6. Step 6: Final answer
    x = 377,942.90

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.