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Finding the Third Proportional to 1,686 and 3,642

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Solution

The third proportional to 1,686 and 3,642 is: 7,867.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,686 : 3,642 = 3,642 : x
  2. Step 2: Convert to fraction form
    1,686/3,642 = 3,642/x
  3. Step 3: Cross multiply
    1,686x = 3,642 × 3,642
  4. Step 4: Simplify right side
    1,686x = 13,264,164
  5. Step 5: Solve for x
    x = 13,264,164/1,686
  6. Step 6: Final answer
    x = 7,867.24

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.