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Finding the Third Proportional to 51,530 and 81,971

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Solution

The third proportional to 51,530 and 81,971 is: 130,394.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,530 : 81,971 = 81,971 : x
  2. Step 2: Convert to fraction form
    51,530/81,971 = 81,971/x
  3. Step 3: Cross multiply
    51,530x = 81,971 × 81,971
  4. Step 4: Simplify right side
    51,530x = 6,719,244,841
  5. Step 5: Solve for x
    x = 6,719,244,841/51,530
  6. Step 6: Final answer
    x = 130,394.82

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.