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Finding the Third Proportional to 51,005 and 77,969

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Solution

The third proportional to 51,005 and 77,969 is: 119,187.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,005 : 77,969 = 77,969 : x
  2. Step 2: Convert to fraction form
    51,005/77,969 = 77,969/x
  3. Step 3: Cross multiply
    51,005x = 77,969 × 77,969
  4. Step 4: Simplify right side
    51,005x = 6,079,164,961
  5. Step 5: Solve for x
    x = 6,079,164,961/51,005
  6. Step 6: Final answer
    x = 119,187.63

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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.