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Finding the Third Proportional to 82,100 and 177,320

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Solution

The third proportional to 82,100 and 177,320 is: 382,976.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,100 : 177,320 = 177,320 : x
  2. Step 2: Convert to fraction form
    82,100/177,320 = 177,320/x
  3. Step 3: Cross multiply
    82,100x = 177,320 × 177,320
  4. Step 4: Simplify right side
    82,100x = 31,442,382,400
  5. Step 5: Solve for x
    x = 31,442,382,400/82,100
  6. Step 6: Final answer
    x = 382,976.64

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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.