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Finding the Third Proportional to 83,471 and 127,970

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Solution

The third proportional to 83,471 and 127,970 is: 196,191.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,471 : 127,970 = 127,970 : x
  2. Step 2: Convert to fraction form
    83,471/127,970 = 127,970/x
  3. Step 3: Cross multiply
    83,471x = 127,970 × 127,970
  4. Step 4: Simplify right side
    83,471x = 16,376,320,900
  5. Step 5: Solve for x
    x = 16,376,320,900/83,471
  6. Step 6: Final answer
    x = 196,191.74

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.