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Finding the Third Proportional to 30,838 and 40,997

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Solution

The third proportional to 30,838 and 40,997 is: 54,502.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,838 : 40,997 = 40,997 : x
  2. Step 2: Convert to fraction form
    30,838/40,997 = 40,997/x
  3. Step 3: Cross multiply
    30,838x = 40,997 × 40,997
  4. Step 4: Simplify right side
    30,838x = 1,680,754,009
  5. Step 5: Solve for x
    x = 1,680,754,009/30,838
  6. Step 6: Final answer
    x = 54,502.69

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.