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Finding the Third Proportional to 13,642 and 20,464

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Solution

The third proportional to 13,642 and 20,464 is: 30,697.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,642 : 20,464 = 20,464 : x
  2. Step 2: Convert to fraction form
    13,642/20,464 = 20,464/x
  3. Step 3: Cross multiply
    13,642x = 20,464 × 20,464
  4. Step 4: Simplify right side
    13,642x = 418,775,296
  5. Step 5: Solve for x
    x = 418,775,296/13,642
  6. Step 6: Final answer
    x = 30,697.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.