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Finding the Third Proportional to 82,084 and 177,128

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Solution

The third proportional to 82,084 and 177,128 is: 382,222.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,084 : 177,128 = 177,128 : x
  2. Step 2: Convert to fraction form
    82,084/177,128 = 177,128/x
  3. Step 3: Cross multiply
    82,084x = 177,128 × 177,128
  4. Step 4: Simplify right side
    82,084x = 31,374,328,384
  5. Step 5: Solve for x
    x = 31,374,328,384/82,084
  6. Step 6: Final answer
    x = 382,222.22

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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.