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Finding the Third Proportional to 81,824 and 176,524

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Solution

The third proportional to 81,824 and 176,524 is: 380,826.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,824 : 176,524 = 176,524 : x
  2. Step 2: Convert to fraction form
    81,824/176,524 = 176,524/x
  3. Step 3: Cross multiply
    81,824x = 176,524 × 176,524
  4. Step 4: Simplify right side
    81,824x = 31,160,722,576
  5. Step 5: Solve for x
    x = 31,160,722,576/81,824
  6. Step 6: Final answer
    x = 380,826.19

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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.