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Finding the Third Proportional to 82,075 and 176,411

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Solution

The third proportional to 82,075 and 176,411 is: 379,175.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,075 : 176,411 = 176,411 : x
  2. Step 2: Convert to fraction form
    82,075/176,411 = 176,411/x
  3. Step 3: Cross multiply
    82,075x = 176,411 × 176,411
  4. Step 4: Simplify right side
    82,075x = 31,120,840,921
  5. Step 5: Solve for x
    x = 31,120,840,921/82,075
  6. Step 6: Final answer
    x = 379,175.64

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.