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Finding the Third Proportional to 205,638 and 311,049

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Solution

The third proportional to 205,638 and 311,049 is: 470,494.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,638 : 311,049 = 311,049 : x
  2. Step 2: Convert to fraction form
    205,638/311,049 = 311,049/x
  3. Step 3: Cross multiply
    205,638x = 311,049 × 311,049
  4. Step 4: Simplify right side
    205,638x = 96,751,480,401
  5. Step 5: Solve for x
    x = 96,751,480,401/205,638
  6. Step 6: Final answer
    x = 470,494.17

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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.