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Finding the Third Proportional to 6,782 and 8,014

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Solution

The third proportional to 6,782 and 8,014 is: 9,469.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,782 : 8,014 = 8,014 : x
  2. Step 2: Convert to fraction form
    6,782/8,014 = 8,014/x
  3. Step 3: Cross multiply
    6,782x = 8,014 × 8,014
  4. Step 4: Simplify right side
    6,782x = 64,224,196
  5. Step 5: Solve for x
    x = 64,224,196/6,782
  6. Step 6: Final answer
    x = 9,469.80

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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.