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Finding the Third Proportional to 3,212 and 6,814

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Solution

The third proportional to 3,212 and 6,814 is: 14,455.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,212 : 6,814 = 6,814 : x
  2. Step 2: Convert to fraction form
    3,212/6,814 = 6,814/x
  3. Step 3: Cross multiply
    3,212x = 6,814 × 6,814
  4. Step 4: Simplify right side
    3,212x = 46,430,596
  5. Step 5: Solve for x
    x = 46,430,596/3,212
  6. Step 6: Final answer
    x = 14,455.35

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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.