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Finding the Third Proportional to 5,914 and 13,684

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Solution

The third proportional to 5,914 and 13,684 is: 31,662.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,914 : 13,684 = 13,684 : x
  2. Step 2: Convert to fraction form
    5,914/13,684 = 13,684/x
  3. Step 3: Cross multiply
    5,914x = 13,684 × 13,684
  4. Step 4: Simplify right side
    5,914x = 187,251,856
  5. Step 5: Solve for x
    x = 187,251,856/5,914
  6. Step 6: Final answer
    x = 31,662.47

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.