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Finding the Third Proportional to 5,782 and 13,642

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Solution

The third proportional to 5,782 and 13,642 is: 32,186.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,782 : 13,642 = 13,642 : x
  2. Step 2: Convert to fraction form
    5,782/13,642 = 13,642/x
  3. Step 3: Cross multiply
    5,782x = 13,642 × 13,642
  4. Step 4: Simplify right side
    5,782x = 186,104,164
  5. Step 5: Solve for x
    x = 186,104,164/5,782
  6. Step 6: Final answer
    x = 32,186.81

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.