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Finding the Third Proportional to 205,972 and 311,862

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Solution

The third proportional to 205,972 and 311,862 is: 472,189.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,972 : 311,862 = 311,862 : x
  2. Step 2: Convert to fraction form
    205,972/311,862 = 311,862/x
  3. Step 3: Cross multiply
    205,972x = 311,862 × 311,862
  4. Step 4: Simplify right side
    205,972x = 97,257,907,044
  5. Step 5: Solve for x
    x = 97,257,907,044/205,972
  6. Step 6: Final answer
    x = 472,189.94

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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.