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Finding the Third Proportional to 5,823 and 10,302

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Solution

The third proportional to 5,823 and 10,302 is: 18,226.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,823 : 10,302 = 10,302 : x
  2. Step 2: Convert to fraction form
    5,823/10,302 = 10,302/x
  3. Step 3: Cross multiply
    5,823x = 10,302 × 10,302
  4. Step 4: Simplify right side
    5,823x = 106,131,204
  5. Step 5: Solve for x
    x = 106,131,204/5,823
  6. Step 6: Final answer
    x = 18,226.21

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.