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Finding the Third Proportional to 37,969 and 83,251

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Solution

The third proportional to 37,969 and 83,251 is: 182,536.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,969 : 83,251 = 83,251 : x
  2. Step 2: Convert to fraction form
    37,969/83,251 = 83,251/x
  3. Step 3: Cross multiply
    37,969x = 83,251 × 83,251
  4. Step 4: Simplify right side
    37,969x = 6,930,729,001
  5. Step 5: Solve for x
    x = 6,930,729,001/37,969
  6. Step 6: Final answer
    x = 182,536.52

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.