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Finding the Third Proportional to 5,206 and 8,286

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Solution

The third proportional to 5,206 and 8,286 is: 13,188.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,206 : 8,286 = 8,286 : x
  2. Step 2: Convert to fraction form
    5,206/8,286 = 8,286/x
  3. Step 3: Cross multiply
    5,206x = 8,286 × 8,286
  4. Step 4: Simplify right side
    5,206x = 68,657,796
  5. Step 5: Solve for x
    x = 68,657,796/5,206
  6. Step 6: Final answer
    x = 13,188.21

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.