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Finding the Third Proportional to 82,099 and 177,295

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Solution

The third proportional to 82,099 and 177,295 is: 382,873.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,099 : 177,295 = 177,295 : x
  2. Step 2: Convert to fraction form
    82,099/177,295 = 177,295/x
  3. Step 3: Cross multiply
    82,099x = 177,295 × 177,295
  4. Step 4: Simplify right side
    82,099x = 31,433,517,025
  5. Step 5: Solve for x
    x = 31,433,517,025/82,099
  6. Step 6: Final answer
    x = 382,873.32

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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.