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Finding the Third Proportional to 5,780 and 8,121

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Solution

The third proportional to 5,780 and 8,121 is: 11,410.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,780 : 8,121 = 8,121 : x
  2. Step 2: Convert to fraction form
    5,780/8,121 = 8,121/x
  3. Step 3: Cross multiply
    5,780x = 8,121 × 8,121
  4. Step 4: Simplify right side
    5,780x = 65,950,641
  5. Step 5: Solve for x
    x = 65,950,641/5,780
  6. Step 6: Final answer
    x = 11,410.15

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.