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Finding the Third Proportional to 8,206 and 12,854

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Solution

The third proportional to 8,206 and 12,854 is: 20,134.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,206 : 12,854 = 12,854 : x
  2. Step 2: Convert to fraction form
    8,206/12,854 = 12,854/x
  3. Step 3: Cross multiply
    8,206x = 12,854 × 12,854
  4. Step 4: Simplify right side
    8,206x = 165,225,316
  5. Step 5: Solve for x
    x = 165,225,316/8,206
  6. Step 6: Final answer
    x = 20,134.70

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.