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Finding the Third Proportional to 6,589 and 14,410

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Solution

The third proportional to 6,589 and 14,410 is: 31,514.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,589 : 14,410 = 14,410 : x
  2. Step 2: Convert to fraction form
    6,589/14,410 = 14,410/x
  3. Step 3: Cross multiply
    6,589x = 14,410 × 14,410
  4. Step 4: Simplify right side
    6,589x = 207,648,100
  5. Step 5: Solve for x
    x = 207,648,100/6,589
  6. Step 6: Final answer
    x = 31,514.36

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.