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Finding the Third Proportional to 12,784 and 27,112

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Solution

The third proportional to 12,784 and 27,112 is: 57,498.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,784 : 27,112 = 27,112 : x
  2. Step 2: Convert to fraction form
    12,784/27,112 = 27,112/x
  3. Step 3: Cross multiply
    12,784x = 27,112 × 27,112
  4. Step 4: Simplify right side
    12,784x = 735,060,544
  5. Step 5: Solve for x
    x = 735,060,544/12,784
  6. Step 6: Final answer
    x = 57,498.48

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.