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Finding the Third Proportional to 746 and 1,729

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Solution

The third proportional to 746 and 1,729 is: 4,007.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    746 : 1,729 = 1,729 : x
  2. Step 2: Convert to fraction form
    746/1,729 = 1,729/x
  3. Step 3: Cross multiply
    746x = 1,729 × 1,729
  4. Step 4: Simplify right side
    746x = 2,989,441
  5. Step 5: Solve for x
    x = 2,989,441/746
  6. Step 6: Final answer
    x = 4,007.29

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.