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Finding the Third Proportional to 8,206 and 9,646

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Solution

The third proportional to 8,206 and 9,646 is: 11,338.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,206 : 9,646 = 9,646 : x
  2. Step 2: Convert to fraction form
    8,206/9,646 = 9,646/x
  3. Step 3: Cross multiply
    8,206x = 9,646 × 9,646
  4. Step 4: Simplify right side
    8,206x = 93,045,316
  5. Step 5: Solve for x
    x = 93,045,316/8,206
  6. Step 6: Final answer
    x = 11,338.69

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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.