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Finding the Third Proportional to 82,114 and 176,506

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Solution

The third proportional to 82,114 and 176,506 is: 379,403.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,114 : 176,506 = 176,506 : x
  2. Step 2: Convert to fraction form
    82,114/176,506 = 176,506/x
  3. Step 3: Cross multiply
    82,114x = 176,506 × 176,506
  4. Step 4: Simplify right side
    82,114x = 31,154,368,036
  5. Step 5: Solve for x
    x = 31,154,368,036/82,114
  6. Step 6: Final answer
    x = 379,403.85

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.