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Finding the Third Proportional to 381,078 and 560,214

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Solution

The third proportional to 381,078 and 560,214 is: 823,557.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    381,078 : 560,214 = 560,214 : x
  2. Step 2: Convert to fraction form
    381,078/560,214 = 560,214/x
  3. Step 3: Cross multiply
    381,078x = 560,214 × 560,214
  4. Step 4: Simplify right side
    381,078x = 313,839,725,796
  5. Step 5: Solve for x
    x = 313,839,725,796/381,078
  6. Step 6: Final answer
    x = 823,557.71

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.