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Finding the Third Proportional to 13,214 and 19,753

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Solution

The third proportional to 13,214 and 19,753 is: 29,527.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,214 : 19,753 = 19,753 : x
  2. Step 2: Convert to fraction form
    13,214/19,753 = 19,753/x
  3. Step 3: Cross multiply
    13,214x = 19,753 × 19,753
  4. Step 4: Simplify right side
    13,214x = 390,181,009
  5. Step 5: Solve for x
    x = 390,181,009/13,214
  6. Step 6: Final answer
    x = 29,527.85

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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.