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Finding the Third Proportional to 105,731 and 232,491

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Solution

The third proportional to 105,731 and 232,491 is: 511,222.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,731 : 232,491 = 232,491 : x
  2. Step 2: Convert to fraction form
    105,731/232,491 = 232,491/x
  3. Step 3: Cross multiply
    105,731x = 232,491 × 232,491
  4. Step 4: Simplify right side
    105,731x = 54,052,065,081
  5. Step 5: Solve for x
    x = 54,052,065,081/105,731
  6. Step 6: Final answer
    x = 511,222.49

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.