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Finding the Third Proportional to 1,684 and 2,966

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Solution

The third proportional to 1,684 and 2,966 is: 5,223.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,684 : 2,966 = 2,966 : x
  2. Step 2: Convert to fraction form
    1,684/2,966 = 2,966/x
  3. Step 3: Cross multiply
    1,684x = 2,966 × 2,966
  4. Step 4: Simplify right side
    1,684x = 8,797,156
  5. Step 5: Solve for x
    x = 8,797,156/1,684
  6. Step 6: Final answer
    x = 5,223.96

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Why These Related Problems?

These problems maintain the same ratio (1.76) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.