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Finding the Third Proportional to 98,770 and 217,231

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Solution

The third proportional to 98,770 and 217,231 is: 477,769.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    98,770 : 217,231 = 217,231 : x
  2. Step 2: Convert to fraction form
    98,770/217,231 = 217,231/x
  3. Step 3: Cross multiply
    98,770x = 217,231 × 217,231
  4. Step 4: Simplify right side
    98,770x = 47,189,307,361
  5. Step 5: Solve for x
    x = 47,189,307,361/98,770
  6. Step 6: Final answer
    x = 477,769.64

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.