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Finding the Third Proportional to 6,474 and 14,406

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Solution

The third proportional to 6,474 and 14,406 is: 32,056.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,474 : 14,406 = 14,406 : x
  2. Step 2: Convert to fraction form
    6,474/14,406 = 14,406/x
  3. Step 3: Cross multiply
    6,474x = 14,406 × 14,406
  4. Step 4: Simplify right side
    6,474x = 207,532,836
  5. Step 5: Solve for x
    x = 207,532,836/6,474
  6. Step 6: Final answer
    x = 32,056.35

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.