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Finding the Third Proportional to 5,876 and 7,834

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Solution

The third proportional to 5,876 and 7,834 is: 10,444.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,876 : 7,834 = 7,834 : x
  2. Step 2: Convert to fraction form
    5,876/7,834 = 7,834/x
  3. Step 3: Cross multiply
    5,876x = 7,834 × 7,834
  4. Step 4: Simplify right side
    5,876x = 61,371,556
  5. Step 5: Solve for x
    x = 61,371,556/5,876
  6. Step 6: Final answer
    x = 10,444.44

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.