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Finding the Third Proportional to 7,782 and 15,834

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Solution

The third proportional to 7,782 and 15,834 is: 32,217.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,782 : 15,834 = 15,834 : x
  2. Step 2: Convert to fraction form
    7,782/15,834 = 15,834/x
  3. Step 3: Cross multiply
    7,782x = 15,834 × 15,834
  4. Step 4: Simplify right side
    7,782x = 250,715,556
  5. Step 5: Solve for x
    x = 250,715,556/7,782
  6. Step 6: Final answer
    x = 32,217.37

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.