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Finding the Third Proportional to 31,517 and 67,206

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Solution

The third proportional to 31,517 and 67,206 is: 143,308.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,517 : 67,206 = 67,206 : x
  2. Step 2: Convert to fraction form
    31,517/67,206 = 67,206/x
  3. Step 3: Cross multiply
    31,517x = 67,206 × 67,206
  4. Step 4: Simplify right side
    31,517x = 4,516,646,436
  5. Step 5: Solve for x
    x = 4,516,646,436/31,517
  6. Step 6: Final answer
    x = 143,308.26

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.