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Finding the Third Proportional to 5,302 and 5,782

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Solution

The third proportional to 5,302 and 5,782 is: 6,305.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,302 : 5,782 = 5,782 : x
  2. Step 2: Convert to fraction form
    5,302/5,782 = 5,782/x
  3. Step 3: Cross multiply
    5,302x = 5,782 × 5,782
  4. Step 4: Simplify right side
    5,302x = 33,431,524
  5. Step 5: Solve for x
    x = 33,431,524/5,302
  6. Step 6: Final answer
    x = 6,305.46

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.