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Finding the Third Proportional to 2,196 and 3,406

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Solution

The third proportional to 2,196 and 3,406 is: 5,282.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,196 : 3,406 = 3,406 : x
  2. Step 2: Convert to fraction form
    2,196/3,406 = 3,406/x
  3. Step 3: Cross multiply
    2,196x = 3,406 × 3,406
  4. Step 4: Simplify right side
    2,196x = 11,600,836
  5. Step 5: Solve for x
    x = 11,600,836/2,196
  6. Step 6: Final answer
    x = 5,282.71

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.