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Finding the Third Proportional to 33,972 and 51,471

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Solution

The third proportional to 33,972 and 51,471 is: 77,983.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    33,972 : 51,471 = 51,471 : x
  2. Step 2: Convert to fraction form
    33,972/51,471 = 51,471/x
  3. Step 3: Cross multiply
    33,972x = 51,471 × 51,471
  4. Step 4: Simplify right side
    33,972x = 2,649,263,841
  5. Step 5: Solve for x
    x = 2,649,263,841/33,972
  6. Step 6: Final answer
    x = 77,983.75

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.