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Finding the Third Proportional to 33,824 and 75,412

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Solution

The third proportional to 33,824 and 75,412 is: 168,134.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    33,824 : 75,412 = 75,412 : x
  2. Step 2: Convert to fraction form
    33,824/75,412 = 75,412/x
  3. Step 3: Cross multiply
    33,824x = 75,412 × 75,412
  4. Step 4: Simplify right side
    33,824x = 5,686,969,744
  5. Step 5: Solve for x
    x = 5,686,969,744/33,824
  6. Step 6: Final answer
    x = 168,134.16

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.