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Finding the Third Proportional to 82,176 and 177,336

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Solution

The third proportional to 82,176 and 177,336 is: 382,691.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,176 : 177,336 = 177,336 : x
  2. Step 2: Convert to fraction form
    82,176/177,336 = 177,336/x
  3. Step 3: Cross multiply
    82,176x = 177,336 × 177,336
  4. Step 4: Simplify right side
    82,176x = 31,448,056,896
  5. Step 5: Solve for x
    x = 31,448,056,896/82,176
  6. Step 6: Final answer
    x = 382,691.50

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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.