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Finding the Third Proportional to 82,416 and 177,972

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Solution

The third proportional to 82,416 and 177,972 is: 384,318.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,416 : 177,972 = 177,972 : x
  2. Step 2: Convert to fraction form
    82,416/177,972 = 177,972/x
  3. Step 3: Cross multiply
    82,416x = 177,972 × 177,972
  4. Step 4: Simplify right side
    82,416x = 31,674,032,784
  5. Step 5: Solve for x
    x = 31,674,032,784/82,416
  6. Step 6: Final answer
    x = 384,318.98

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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.