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Finding the Third Proportional to 82,852 and 177,312

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Solution

The third proportional to 82,852 and 177,312 is: 379,466.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,852 : 177,312 = 177,312 : x
  2. Step 2: Convert to fraction form
    82,852/177,312 = 177,312/x
  3. Step 3: Cross multiply
    82,852x = 177,312 × 177,312
  4. Step 4: Simplify right side
    82,852x = 31,439,545,344
  5. Step 5: Solve for x
    x = 31,439,545,344/82,852
  6. Step 6: Final answer
    x = 379,466.34

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.