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Finding the Third Proportional to 82,380 and 177,396

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Solution

The third proportional to 82,380 and 177,396 is: 382,002.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,380 : 177,396 = 177,396 : x
  2. Step 2: Convert to fraction form
    82,380/177,396 = 177,396/x
  3. Step 3: Cross multiply
    82,380x = 177,396 × 177,396
  4. Step 4: Simplify right side
    82,380x = 31,469,340,816
  5. Step 5: Solve for x
    x = 31,469,340,816/82,380
  6. Step 6: Final answer
    x = 382,002.19

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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.