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Finding the Third Proportional to 205,984 and 311,879

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Solution

The third proportional to 205,984 and 311,879 is: 472,213.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,984 : 311,879 = 311,879 : x
  2. Step 2: Convert to fraction form
    205,984/311,879 = 311,879/x
  3. Step 3: Cross multiply
    205,984x = 311,879 × 311,879
  4. Step 4: Simplify right side
    205,984x = 97,268,510,641
  5. Step 5: Solve for x
    x = 97,268,510,641/205,984
  6. Step 6: Final answer
    x = 472,213.91

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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.