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Finding the Third Proportional to 21,729 and 32,199

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Solution

The third proportional to 21,729 and 32,199 is: 47,713.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,729 : 32,199 = 32,199 : x
  2. Step 2: Convert to fraction form
    21,729/32,199 = 32,199/x
  3. Step 3: Cross multiply
    21,729x = 32,199 × 32,199
  4. Step 4: Simplify right side
    21,729x = 1,036,775,601
  5. Step 5: Solve for x
    x = 1,036,775,601/21,729
  6. Step 6: Final answer
    x = 47,713.91

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.