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Finding the Third Proportional to 82,210 and 177,512

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Solution

The third proportional to 82,210 and 177,512 is: 383,292.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,210 : 177,512 = 177,512 : x
  2. Step 2: Convert to fraction form
    82,210/177,512 = 177,512/x
  3. Step 3: Cross multiply
    82,210x = 177,512 × 177,512
  4. Step 4: Simplify right side
    82,210x = 31,510,510,144
  5. Step 5: Solve for x
    x = 31,510,510,144/82,210
  6. Step 6: Final answer
    x = 383,292.91

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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.