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Finding the Third Proportional to 137,972 and 208,038

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Solution

The third proportional to 137,972 and 208,038 is: 313,685.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    137,972 : 208,038 = 208,038 : x
  2. Step 2: Convert to fraction form
    137,972/208,038 = 208,038/x
  3. Step 3: Cross multiply
    137,972x = 208,038 × 208,038
  4. Step 4: Simplify right side
    137,972x = 43,279,809,444
  5. Step 5: Solve for x
    x = 43,279,809,444/137,972
  6. Step 6: Final answer
    x = 313,685.45

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.