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Finding the Third Proportional to 137,974 and 208,041

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Solution

The third proportional to 137,974 and 208,041 is: 313,689.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    137,974 : 208,041 = 208,041 : x
  2. Step 2: Convert to fraction form
    137,974/208,041 = 208,041/x
  3. Step 3: Cross multiply
    137,974x = 208,041 × 208,041
  4. Step 4: Simplify right side
    137,974x = 43,281,057,681
  5. Step 5: Solve for x
    x = 43,281,057,681/137,974
  6. Step 6: Final answer
    x = 313,689.95

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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.