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Finding the Third Proportional to 1,686 and 2,563

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Solution

The third proportional to 1,686 and 2,563 is: 3,896.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,686 : 2,563 = 2,563 : x
  2. Step 2: Convert to fraction form
    1,686/2,563 = 2,563/x
  3. Step 3: Cross multiply
    1,686x = 2,563 × 2,563
  4. Step 4: Simplify right side
    1,686x = 6,568,969
  5. Step 5: Solve for x
    x = 6,568,969/1,686
  6. Step 6: Final answer
    x = 3,896.19

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.