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Finding the Third Proportional to 197,024 and 420,256

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Solution

The third proportional to 197,024 and 420,256 is: 896,414.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,024 : 420,256 = 420,256 : x
  2. Step 2: Convert to fraction form
    197,024/420,256 = 420,256/x
  3. Step 3: Cross multiply
    197,024x = 420,256 × 420,256
  4. Step 4: Simplify right side
    197,024x = 176,615,105,536
  5. Step 5: Solve for x
    x = 176,615,105,536/197,024
  6. Step 6: Final answer
    x = 896,414.17

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.