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Finding the Third Proportional to 13,738 and 20,514

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Solution

The third proportional to 13,738 and 20,514 is: 30,632.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,738 : 20,514 = 20,514 : x
  2. Step 2: Convert to fraction form
    13,738/20,514 = 20,514/x
  3. Step 3: Cross multiply
    13,738x = 20,514 × 20,514
  4. Step 4: Simplify right side
    13,738x = 420,824,196
  5. Step 5: Solve for x
    x = 420,824,196/13,738
  6. Step 6: Final answer
    x = 30,632.13

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.