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Finding the Third Proportional to 3,659 and 5,214

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Solution

The third proportional to 3,659 and 5,214 is: 7,429.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,659 : 5,214 = 5,214 : x
  2. Step 2: Convert to fraction form
    3,659/5,214 = 5,214/x
  3. Step 3: Cross multiply
    3,659x = 5,214 × 5,214
  4. Step 4: Simplify right side
    3,659x = 27,185,796
  5. Step 5: Solve for x
    x = 27,185,796/3,659
  6. Step 6: Final answer
    x = 7,429.84

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.