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Finding the Third Proportional to 5,914 and 8,412

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Solution

The third proportional to 5,914 and 8,412 is: 11,965.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,914 : 8,412 = 8,412 : x
  2. Step 2: Convert to fraction form
    5,914/8,412 = 8,412/x
  3. Step 3: Cross multiply
    5,914x = 8,412 × 8,412
  4. Step 4: Simplify right side
    5,914x = 70,761,744
  5. Step 5: Solve for x
    x = 70,761,744/5,914
  6. Step 6: Final answer
    x = 11,965.12

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.