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Finding the Third Proportional to 6,412 and 13,816

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Solution

The third proportional to 6,412 and 13,816 is: 29,769.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,412 : 13,816 = 13,816 : x
  2. Step 2: Convert to fraction form
    6,412/13,816 = 13,816/x
  3. Step 3: Cross multiply
    6,412x = 13,816 × 13,816
  4. Step 4: Simplify right side
    6,412x = 190,881,856
  5. Step 5: Solve for x
    x = 190,881,856/6,412
  6. Step 6: Final answer
    x = 29,769.47

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.