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Finding the Third Proportional to 271,824 and 419,856

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Solution

The third proportional to 271,824 and 419,856 is: 648,504.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    271,824 : 419,856 = 419,856 : x
  2. Step 2: Convert to fraction form
    271,824/419,856 = 419,856/x
  3. Step 3: Cross multiply
    271,824x = 419,856 × 419,856
  4. Step 4: Simplify right side
    271,824x = 176,279,060,736
  5. Step 5: Solve for x
    x = 176,279,060,736/271,824
  6. Step 6: Final answer
    x = 648,504.40

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.