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Finding the Third Proportional to 100,345 and 217,231

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Solution

The third proportional to 100,345 and 217,231 is: 470,270.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,345 : 217,231 = 217,231 : x
  2. Step 2: Convert to fraction form
    100,345/217,231 = 217,231/x
  3. Step 3: Cross multiply
    100,345x = 217,231 × 217,231
  4. Step 4: Simplify right side
    100,345x = 47,189,307,361
  5. Step 5: Solve for x
    x = 47,189,307,361/100,345
  6. Step 6: Final answer
    x = 470,270.64

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.