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Finding the Third Proportional to 2,478 and 5,414

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Solution

The third proportional to 2,478 and 5,414 is: 11,828.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,478 : 5,414 = 5,414 : x
  2. Step 2: Convert to fraction form
    2,478/5,414 = 5,414/x
  3. Step 3: Cross multiply
    2,478x = 5,414 × 5,414
  4. Step 4: Simplify right side
    2,478x = 29,311,396
  5. Step 5: Solve for x
    x = 29,311,396/2,478
  6. Step 6: Final answer
    x = 11,828.65

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.