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Finding the Third Proportional to 120,206 and 214,168

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Solution

The third proportional to 120,206 and 214,168 is: 381,577.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,206 : 214,168 = 214,168 : x
  2. Step 2: Convert to fraction form
    120,206/214,168 = 214,168/x
  3. Step 3: Cross multiply
    120,206x = 214,168 × 214,168
  4. Step 4: Simplify right side
    120,206x = 45,867,932,224
  5. Step 5: Solve for x
    x = 45,867,932,224/120,206
  6. Step 6: Final answer
    x = 381,577.73

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.