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Finding the Third Proportional to 81,974 and 180,025

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Solution

The third proportional to 81,974 and 180,025 is: 395,357.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,974 : 180,025 = 180,025 : x
  2. Step 2: Convert to fraction form
    81,974/180,025 = 180,025/x
  3. Step 3: Cross multiply
    81,974x = 180,025 × 180,025
  4. Step 4: Simplify right side
    81,974x = 32,409,000,625
  5. Step 5: Solve for x
    x = 32,409,000,625/81,974
  6. Step 6: Final answer
    x = 395,357.07

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.