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Finding the Third Proportional to 2,186 and 5,069

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Solution

The third proportional to 2,186 and 5,069 is: 11,754.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,186 : 5,069 = 5,069 : x
  2. Step 2: Convert to fraction form
    2,186/5,069 = 5,069/x
  3. Step 3: Cross multiply
    2,186x = 5,069 × 5,069
  4. Step 4: Simplify right side
    2,186x = 25,694,761
  5. Step 5: Solve for x
    x = 25,694,761/2,186
  6. Step 6: Final answer
    x = 11,754.24

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.