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Finding the Third Proportional to 262,082 and 419,731

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Solution

The third proportional to 262,082 and 419,731 is: 672,209.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,082 : 419,731 = 419,731 : x
  2. Step 2: Convert to fraction form
    262,082/419,731 = 419,731/x
  3. Step 3: Cross multiply
    262,082x = 419,731 × 419,731
  4. Step 4: Simplify right side
    262,082x = 176,174,112,361
  5. Step 5: Solve for x
    x = 176,174,112,361/262,082
  6. Step 6: Final answer
    x = 672,209.89

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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.