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Finding the Third Proportional to 31,521 and 67,214

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Solution

The third proportional to 31,521 and 67,214 is: 143,324.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,521 : 67,214 = 67,214 : x
  2. Step 2: Convert to fraction form
    31,521/67,214 = 67,214/x
  3. Step 3: Cross multiply
    31,521x = 67,214 × 67,214
  4. Step 4: Simplify right side
    31,521x = 4,517,721,796
  5. Step 5: Solve for x
    x = 4,517,721,796/31,521
  6. Step 6: Final answer
    x = 143,324.19

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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.