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Finding the Third Proportional to 8,414 and 17,853

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Solution

The third proportional to 8,414 and 17,853 is: 37,880.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,414 : 17,853 = 17,853 : x
  2. Step 2: Convert to fraction form
    8,414/17,853 = 17,853/x
  3. Step 3: Cross multiply
    8,414x = 17,853 × 17,853
  4. Step 4: Simplify right side
    8,414x = 318,729,609
  5. Step 5: Solve for x
    x = 318,729,609/8,414
  6. Step 6: Final answer
    x = 37,880.87

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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.