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Finding the Third Proportional to 83,214 and 127,902

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Solution

The third proportional to 83,214 and 127,902 is: 196,588.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,214 : 127,902 = 127,902 : x
  2. Step 2: Convert to fraction form
    83,214/127,902 = 127,902/x
  3. Step 3: Cross multiply
    83,214x = 127,902 × 127,902
  4. Step 4: Simplify right side
    83,214x = 16,358,921,604
  5. Step 5: Solve for x
    x = 16,358,921,604/83,214
  6. Step 6: Final answer
    x = 196,588.57

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.