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Finding the Third Proportional to 119,729 and 180,096

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Solution

The third proportional to 119,729 and 180,096 is: 270,899.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    119,729 : 180,096 = 180,096 : x
  2. Step 2: Convert to fraction form
    119,729/180,096 = 180,096/x
  3. Step 3: Cross multiply
    119,729x = 180,096 × 180,096
  4. Step 4: Simplify right side
    119,729x = 32,434,569,216
  5. Step 5: Solve for x
    x = 32,434,569,216/119,729
  6. Step 6: Final answer
    x = 270,899.86

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.