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Finding the Third Proportional to 7,674 and 16,406

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Solution

The third proportional to 7,674 and 16,406 is: 35,073.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,674 : 16,406 = 16,406 : x
  2. Step 2: Convert to fraction form
    7,674/16,406 = 16,406/x
  3. Step 3: Cross multiply
    7,674x = 16,406 × 16,406
  4. Step 4: Simplify right side
    7,674x = 269,156,836
  5. Step 5: Solve for x
    x = 269,156,836/7,674
  6. Step 6: Final answer
    x = 35,073.86

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.