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Finding the Third Proportional to 83,971 and 127,961

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Solution

The third proportional to 83,971 and 127,961 is: 194,996.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,971 : 127,961 = 127,961 : x
  2. Step 2: Convert to fraction form
    83,971/127,961 = 127,961/x
  3. Step 3: Cross multiply
    83,971x = 127,961 × 127,961
  4. Step 4: Simplify right side
    83,971x = 16,374,017,521
  5. Step 5: Solve for x
    x = 16,374,017,521/83,971
  6. Step 6: Final answer
    x = 194,996.10

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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.