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Finding the Third Proportional to 4,006 and 5,729

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Solution

The third proportional to 4,006 and 5,729 is: 8,193.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,006 : 5,729 = 5,729 : x
  2. Step 2: Convert to fraction form
    4,006/5,729 = 5,729/x
  3. Step 3: Cross multiply
    4,006x = 5,729 × 5,729
  4. Step 4: Simplify right side
    4,006x = 32,821,441
  5. Step 5: Solve for x
    x = 32,821,441/4,006
  6. Step 6: Final answer
    x = 8,193.07

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.