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Finding the Third Proportional to 205,981 and 311,874

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Solution

The third proportional to 205,981 and 311,874 is: 472,205.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,981 : 311,874 = 311,874 : x
  2. Step 2: Convert to fraction form
    205,981/311,874 = 311,874/x
  3. Step 3: Cross multiply
    205,981x = 311,874 × 311,874
  4. Step 4: Simplify right side
    205,981x = 97,265,391,876
  5. Step 5: Solve for x
    x = 97,265,391,876/205,981
  6. Step 6: Final answer
    x = 472,205.65

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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.