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Finding the Third Proportional to 8,194 and 9,670

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Solution

The third proportional to 8,194 and 9,670 is: 11,411.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,194 : 9,670 = 9,670 : x
  2. Step 2: Convert to fraction form
    8,194/9,670 = 9,670/x
  3. Step 3: Cross multiply
    8,194x = 9,670 × 9,670
  4. Step 4: Simplify right side
    8,194x = 93,508,900
  5. Step 5: Solve for x
    x = 93,508,900/8,194
  6. Step 6: Final answer
    x = 11,411.87

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.