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Finding the Third Proportional to 82,064 and 177,952

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Solution

The third proportional to 82,064 and 177,952 is: 385,880.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,064 : 177,952 = 177,952 : x
  2. Step 2: Convert to fraction form
    82,064/177,952 = 177,952/x
  3. Step 3: Cross multiply
    82,064x = 177,952 × 177,952
  4. Step 4: Simplify right side
    82,064x = 31,666,914,304
  5. Step 5: Solve for x
    x = 31,666,914,304/82,064
  6. Step 6: Final answer
    x = 385,880.71

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.