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Finding the Third Proportional to 82,824 and 110,349

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Solution

The third proportional to 82,824 and 110,349 is: 147,021.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,824 : 110,349 = 110,349 : x
  2. Step 2: Convert to fraction form
    82,824/110,349 = 110,349/x
  3. Step 3: Cross multiply
    82,824x = 110,349 × 110,349
  4. Step 4: Simplify right side
    82,824x = 12,176,901,801
  5. Step 5: Solve for x
    x = 12,176,901,801/82,824
  6. Step 6: Final answer
    x = 147,021.42

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.