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Finding the Third Proportional to 82,078 and 176,416

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Solution

The third proportional to 82,078 and 176,416 is: 379,183.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,078 : 176,416 = 176,416 : x
  2. Step 2: Convert to fraction form
    82,078/176,416 = 176,416/x
  3. Step 3: Cross multiply
    82,078x = 176,416 × 176,416
  4. Step 4: Simplify right side
    82,078x = 31,122,605,056
  5. Step 5: Solve for x
    x = 31,122,605,056/82,078
  6. Step 6: Final answer
    x = 379,183.28

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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.