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Finding the Third Proportional to 102,238 and 209,576

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Solution

The third proportional to 102,238 and 209,576 is: 429,606.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,238 : 209,576 = 209,576 : x
  2. Step 2: Convert to fraction form
    102,238/209,576 = 209,576/x
  3. Step 3: Cross multiply
    102,238x = 209,576 × 209,576
  4. Step 4: Simplify right side
    102,238x = 43,922,099,776
  5. Step 5: Solve for x
    x = 43,922,099,776/102,238
  6. Step 6: Final answer
    x = 429,606.41

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.