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Finding the Third Proportional to 262,080 and 419,728

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Solution

The third proportional to 262,080 and 419,728 is: 672,205.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,080 : 419,728 = 419,728 : x
  2. Step 2: Convert to fraction form
    262,080/419,728 = 419,728/x
  3. Step 3: Cross multiply
    262,080x = 419,728 × 419,728
  4. Step 4: Simplify right side
    262,080x = 176,171,593,984
  5. Step 5: Solve for x
    x = 176,171,593,984/262,080
  6. Step 6: Final answer
    x = 672,205.41

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.