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Finding the Third Proportional to 1,729 and 3,669

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Solution

The third proportional to 1,729 and 3,669 is: 7,785.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,729 : 3,669 = 3,669 : x
  2. Step 2: Convert to fraction form
    1,729/3,669 = 3,669/x
  3. Step 3: Cross multiply
    1,729x = 3,669 × 3,669
  4. Step 4: Simplify right side
    1,729x = 13,461,561
  5. Step 5: Solve for x
    x = 13,461,561/1,729
  6. Step 6: Final answer
    x = 7,785.75

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.