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Finding the Third Proportional to 6,814 and 7,786

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Solution

The third proportional to 6,814 and 7,786 is: 8,896.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,814 : 7,786 = 7,786 : x
  2. Step 2: Convert to fraction form
    6,814/7,786 = 7,786/x
  3. Step 3: Cross multiply
    6,814x = 7,786 × 7,786
  4. Step 4: Simplify right side
    6,814x = 60,621,796
  5. Step 5: Solve for x
    x = 60,621,796/6,814
  6. Step 6: Final answer
    x = 8,896.65

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.