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Finding the Third Proportional to 13,574 and 27,814

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Solution

The third proportional to 13,574 and 27,814 is: 56,992.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,574 : 27,814 = 27,814 : x
  2. Step 2: Convert to fraction form
    13,574/27,814 = 27,814/x
  3. Step 3: Cross multiply
    13,574x = 27,814 × 27,814
  4. Step 4: Simplify right side
    13,574x = 773,618,596
  5. Step 5: Solve for x
    x = 773,618,596/13,574
  6. Step 6: Final answer
    x = 56,992.68

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.