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Finding the Third Proportional to 120,138 and 180,207

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Solution

The third proportional to 120,138 and 180,207 is: 270,310.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,138 : 180,207 = 180,207 : x
  2. Step 2: Convert to fraction form
    120,138/180,207 = 180,207/x
  3. Step 3: Cross multiply
    120,138x = 180,207 × 180,207
  4. Step 4: Simplify right side
    120,138x = 32,474,562,849
  5. Step 5: Solve for x
    x = 32,474,562,849/120,138
  6. Step 6: Final answer
    x = 270,310.50

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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.