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Finding the Third Proportional to 11,414 and 24,286

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Solution

The third proportional to 11,414 and 24,286 is: 51,674.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    11,414 : 24,286 = 24,286 : x
  2. Step 2: Convert to fraction form
    11,414/24,286 = 24,286/x
  3. Step 3: Cross multiply
    11,414x = 24,286 × 24,286
  4. Step 4: Simplify right side
    11,414x = 589,809,796
  5. Step 5: Solve for x
    x = 589,809,796/11,414
  6. Step 6: Final answer
    x = 51,674.24

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.