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Finding the Third Proportional to 57,434 and 82,221

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Solution

The third proportional to 57,434 and 82,221 is: 117,705.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    57,434 : 82,221 = 82,221 : x
  2. Step 2: Convert to fraction form
    57,434/82,221 = 82,221/x
  3. Step 3: Cross multiply
    57,434x = 82,221 × 82,221
  4. Step 4: Simplify right side
    57,434x = 6,760,292,841
  5. Step 5: Solve for x
    x = 6,760,292,841/57,434
  6. Step 6: Final answer
    x = 117,705.42

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.