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Finding the Third Proportional to 54,024 and 81,780

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Solution

The third proportional to 54,024 and 81,780 is: 123,796.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,024 : 81,780 = 81,780 : x
  2. Step 2: Convert to fraction form
    54,024/81,780 = 81,780/x
  3. Step 3: Cross multiply
    54,024x = 81,780 × 81,780
  4. Step 4: Simplify right side
    54,024x = 6,687,968,400
  5. Step 5: Solve for x
    x = 6,687,968,400/54,024
  6. Step 6: Final answer
    x = 123,796.25

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.