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Finding the Third Proportional to 103,414 and 213,295

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Solution

The third proportional to 103,414 and 213,295 is: 439,928.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    103,414 : 213,295 = 213,295 : x
  2. Step 2: Convert to fraction form
    103,414/213,295 = 213,295/x
  3. Step 3: Cross multiply
    103,414x = 213,295 × 213,295
  4. Step 4: Simplify right side
    103,414x = 45,494,757,025
  5. Step 5: Solve for x
    x = 45,494,757,025/103,414
  6. Step 6: Final answer
    x = 439,928.41

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.