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Finding the Third Proportional to 7,694 and 8,414

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Solution

The third proportional to 7,694 and 8,414 is: 9,201.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,694 : 8,414 = 8,414 : x
  2. Step 2: Convert to fraction form
    7,694/8,414 = 8,414/x
  3. Step 3: Cross multiply
    7,694x = 8,414 × 8,414
  4. Step 4: Simplify right side
    7,694x = 70,795,396
  5. Step 5: Solve for x
    x = 70,795,396/7,694
  6. Step 6: Final answer
    x = 9,201.38

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.