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Finding the Third Proportional to 5,906 and 8,229

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Solution

The third proportional to 5,906 and 8,229 is: 11,465.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,906 : 8,229 = 8,229 : x
  2. Step 2: Convert to fraction form
    5,906/8,229 = 8,229/x
  3. Step 3: Cross multiply
    5,906x = 8,229 × 8,229
  4. Step 4: Simplify right side
    5,906x = 67,716,441
  5. Step 5: Solve for x
    x = 67,716,441/5,906
  6. Step 6: Final answer
    x = 11,465.70

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.