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Finding the Third Proportional to 2,414 and 5,837

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Solution

The third proportional to 2,414 and 5,837 is: 14,113.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,414 : 5,837 = 5,837 : x
  2. Step 2: Convert to fraction form
    2,414/5,837 = 5,837/x
  3. Step 3: Cross multiply
    2,414x = 5,837 × 5,837
  4. Step 4: Simplify right side
    2,414x = 34,070,569
  5. Step 5: Solve for x
    x = 34,070,569/2,414
  6. Step 6: Final answer
    x = 14,113.74

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.