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Finding the Third Proportional to 137,646 and 193,824

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Solution

The third proportional to 137,646 and 193,824 is: 272,930.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    137,646 : 193,824 = 193,824 : x
  2. Step 2: Convert to fraction form
    137,646/193,824 = 193,824/x
  3. Step 3: Cross multiply
    137,646x = 193,824 × 193,824
  4. Step 4: Simplify right side
    137,646x = 37,567,742,976
  5. Step 5: Solve for x
    x = 37,567,742,976/137,646
  6. Step 6: Final answer
    x = 272,930.15

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.