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Finding the Third Proportional to 591 and 1,431

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Solution

The third proportional to 591 and 1,431 is: 3,464.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    591 : 1,431 = 1,431 : x
  2. Step 2: Convert to fraction form
    591/1,431 = 1,431/x
  3. Step 3: Cross multiply
    591x = 1,431 × 1,431
  4. Step 4: Simplify right side
    591x = 2,047,761
  5. Step 5: Solve for x
    x = 2,047,761/591
  6. Step 6: Final answer
    x = 3,464.91

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.