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Finding the Third Proportional to 19,729 and 31,232

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Solution

The third proportional to 19,729 and 31,232 is: 49,441.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,729 : 31,232 = 31,232 : x
  2. Step 2: Convert to fraction form
    19,729/31,232 = 31,232/x
  3. Step 3: Cross multiply
    19,729x = 31,232 × 31,232
  4. Step 4: Simplify right side
    19,729x = 975,437,824
  5. Step 5: Solve for x
    x = 975,437,824/19,729
  6. Step 6: Final answer
    x = 49,441.83

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.