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Finding the Third Proportional to 5,286 and 8,499

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Solution

The third proportional to 5,286 and 8,499 is: 13,664.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,286 : 8,499 = 8,499 : x
  2. Step 2: Convert to fraction form
    5,286/8,499 = 8,499/x
  3. Step 3: Cross multiply
    5,286x = 8,499 × 8,499
  4. Step 4: Simplify right side
    5,286x = 72,233,001
  5. Step 5: Solve for x
    x = 72,233,001/5,286
  6. Step 6: Final answer
    x = 13,664.96

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.